The US Centers for Disease Control and Prevention (CDC), in 2019, designated Methicillin-resistant Staphylococcus aureus (MRSA) as a serious antimicrobial resistance threat. The risk of acquiring MRSA and suffering life-threatening consequences due to it remains especially high for hospitalized patients due to a unique combination of factors, including: co-morbid conditions, immuno suppression, antibiotic use, and risk of contact with contaminated hospital workers and equipment. In this paper, we present a novel generative probabilistic model, GenHAI, for modeling sequences of MRSA test results outcomes for patients during a single hospitalization. This model can be used to answer many important questions from the perspectives of hospital administrators for mitigating the risk of MRSA infections. Our model is based on the probabilistic programming paradigm, and can be used to approximately answer a variety of predictive, causal, and counterfactual questions. We demonstrate the efficacy of our model by comparing it against discriminative and generative machine learning models using two real-world datasets.

Estimating the true prevalence of an epidemic outbreak is a key public health problem. This is challenging because surveillance is usually resource intensive and biased. In the network setting, prior work on cost sensitive disease surveillance has focused on choosing a subset of individuals (or nodes) to minimize objectives such as probability of outbreak detection. Such methods do not give insights into the outbreak size distribution which, despite being complex and multi-modal, is very useful in public health planning. We introduce TESTPREV, a problem of choosing a subset of nodes which maximizes the mutual information with disease prevalence, which directly provides information about the outbreak size distribution. We show that, under the independent cascade (IC) model, solutions computed by all prior disease surveillance approaches are highly sub-optimal for TESTPREV in general. We also show that TESTPREV is hard to even approximate. While this mutual information objective is computationally challenging for general networks, we show that it can be computed efficiently for various network classes. We present a greedy strategy, called GREEDYMI, that uses estimates of mutual information from cascade simulations and thus can be applied on any network and disease model. We find that GREEDYMI does better than natural baselines in terms of maximizing the mutual information as well as reducing the expected variance in outbreak size, under the IC model.

Diffusion models are vulnerable to backdoor attacks, where malicious attackers inject backdoors by poisoning certain training samples during the training stage. This poses a significant threat to real-world applications in the Model-as-a-Service (MaaS) scenario, where users query diffusion models through APIs or directly download them from the internet. To mitigate the threat of backdoor attacks under MaaS, black-box input-level backdoor detection has drawn recent interest, where defenders aim to build a firewall that filters out backdoor samples in the inference stage, with access only to input queries and the generated results from diffusion models. Despite some preliminary explorations on the traditional classification tasks, these methods cannot be directly applied to the generative tasks due to two major challenges: (1) more diverse failures and (2) a multi-modality attack surface. In this paper, we propose a black-box input-level backdoor detection framework on diffusion models, called UFID. Our defense is motivated by an insightful causal analysis: Backdoor attacks serve as the confounder, introducing a spurious path from input to target images, which remains consistent even when we perturb the input samples with Gaussian noise. We further validate the intuition with theoretical analysis. Extensive experiments across different datasets on both conditional and unconditional diffusion models show that our method achieves superb performance on detection effectiveness and run-time efficiency.

Consider public health officials aiming to spread awareness about a new vaccine in a community interconnected by a social network. How can they distribute information with minimal resources, so as to avoid polarization and ensure community-wide convergence of opinion? To tackle such challenges, we initiate the study of sample complexity of opinion formation in networks. Our framework is built on the recognized opinion formation game, where we regard each agent’s opinion as a data-derived model, unlike previous works that treat opinions as data-independent scalars. The opinion model for every agent is initially learned from its local samples and evolves game-theoretically as all agents communicate with neighbors and revise their models towards an equilibrium. Our focus is on the sample complexity needed to ensure that the opinions converge to an equilibrium such that every agent’s final model has low generalization error. Our paper has two main technical results. First, we present a novel polynomial time optimization framework to quantify the total sample complexity for arbitrary networks, when the underlying learning problem is (generalized) linear regression. Second, we leverage this optimization to study the network gain which measures the improvement of sample complexity when learning over a network compared to that in isolation. Towards this end, we derive network gain bounds for various network classes including cliques, star graphs, and random regular graphs. Additionally, our framework provides a method to study sample distribution within the network, suggesting that it is sufficient to allocate samples inversely to the degree. Empirical results on both synthetic and real-world networks strongly support our theoretical findings.

Anti-backdoor learning, aiming to train clean models directly from poisoned datasets, serves as an important defense method for backdoor attack. However, existing methods usually fail to recover backdoored samples to their original, correct labels and suffer from poor generalization to large pre-trained models due to its non end-to end training, making them unsuitable for protecting the increasingly prevalent large pre-trained models. To bridge the gap, we first revisit the anti-backdoor learning problem from a causal perspective. Our theoretical causal analysis reveals that incorporating \emph{\textbf{both}} images and the associated attack indicators preserves the model's integrity. Building on the theoretical analysis, we introduce an end-to-end method, Mind Control through Causal Inference (MCCI), to train clean models directly from poisoned datasets. This approach leverages both the image and the attack indicator to train the model. Based on this training paradigm, the model’s perception of whether an input is clean or backdoored can be controlled. Typically, by introducing fake non-attack indicators, the model perceives all inputs as clean and makes correct predictions, even for poisoned samples. Extensive experiments demonstrate that our method achieves state-of-the-art performance, efficiently recovering the original correct predictions for poisoned samples and enhancing accuracy on clean samples.

Recent studies have uncovered a troubling vulnerability in the fine-tuning stage of large language models (LLMs): even fine-tuning on entirely benign datasets can lead to a significant increase in the harmfulness of LLM outputs. Building on this finding, our red teaming study takes this threat one step further by developing a more effective attack. Specifically, we analyze and identify samples within benign datasets that contribute most to safety degradation, then fine-tune LLMs exclusively on these samples. We approach this problem from an outlier detection perspective and propose Self-Inf-N, to detect and extract outliers for fine-tuning. Our findings reveal that fine-tuning LLMs on 100 outlier samples selected by Self-Inf-N in the benign datasets severely compromises LLM safety alignment. Extensive experiments across seven mainstream LLMs demonstrate that our attack exhibits high transferability across different architectures and remains effective in practical scenarios. Alarmingly, our results indicate that most existing mitigation strategies fail to defend against this attack, underscoring the urgent need for more robust alignment safeguards. Codes are available at https://github.com/GuanZihan/Benign-Samples-Matter.

We study exascale parallel algorithms for the selection of intervention or monitoring strategies in massive realistic socio-technical networks through scalable Influence Maximization (InfMax) algorithms.We employ novel techniques to enable efficient scaling on up to 8k nodes of OLCF Frontier, with 65k AMD GPUs and 458k AMD CPU cores.Current state-of-the-art InfMax tools are limited to networks with only a few million actors (vertices) and a few hundred million interactions (edges).By overcoming these limitations, ICS '25, June 08-11, 2025, Salt Lake City, UT, USA Minutoli et al.we show that our approach is capable of processing a realistic social contact network of the United States with 285 million nodes and about 8 billion edges.This two ordersof-magnitude improvement over the previous state-of-theart is obtained by leveraging algorithmic advancements for the InfMax problem and designing several problem-specific approaches to overlap communication with computation, improve GPU efficiency, and lower the application's memory requirements.We evaluate strong scaling for computing 10k most influential seeds using up to 8k nodes of an exascale system, and weak scaling from 128 to 8k system nodes for seed sets ranging from 625 to 40k seeds.We achieve the fastest-known runtime of 25 minutes while performing 48 million diffusion simulations totaling 2.31 petabytes to identify 40k influential seeds using 8k nodes, and take 5.75 minutes to identify 10k seeds while using 4k nodes.

Designing effective strategies for controlling epidemic spread by vaccination is an important question in epidemiology, especially in the early stages when vaccines are limited. This is a challenging question when the contact network is very heterogeneous, and strategies based on controlling network properties, such as the degree and spectral radius, have been shown to be effective. Implementation of such strategies requires detailed information on the contact structure, which might be sensitive in many applications. Our focus here is on choosing effective vaccination strategies when the edges are sensitive and differential privacy guarantees are needed. Our main contributions are $(\varepsilon,\delta)$-differentially private algorithms for designing vaccination strategies by reducing the maximum degree and spectral radius. Our key technique is a private algorithm for the multi-set multi-cover problem, which we use for controlling network properties. We evaluate privacy-utility tradeoffs of our algorithms on multiple synthetic and real-world networks, and show their effectiveness.

One of the most significant challenges in combating against the spread of infectious diseases was the difficulty in estimating the true magnitude of infections. Unreported infections could drive up disease spread, making it very hard to accurately estimate the infectivity of the pathogen, therewith hampering our ability to react effectively. Despite the use of surveillance-based methods such as serological studies, identifying the true magnitude is still challenging. This paper proposes an information theoretic approach for accurately estimating the number of total infections. Our approach is built on top of Ordinary Differential Equations (ODE) based models, which are commonly used in epidemiology and for estimating such infections. We show how we can help such models to better compute the number of total infections and identify the parametrization by which we need the fewest bits to describe the observed dynamics of reported infections. Our experiments on COVID-19 spread show that our approach leads to not only substantially better estimates of the number of total infections but also better forecasts of infections than standard model calibration based methods. We additionally show how our learned parametrization helps in modeling more accurate what-if scenarios with non-pharmaceutical interventions. Our approach provides a general method for improving epidemic modeling which is applicable broadly.

Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying network is known. In this work, we focus on a more challenging setting: to learn both the behavior and the underlying topology of a black-box system. We show that, in general, this learning problem is computationally intractable. On the positive side, we present efficient learning methods under the PAC model when the underlying graph of the dynamical system belongs to certain classes. Further, we examine a relaxed setting where the topology of an unknown system is partially observed. For this case, we develop an efficient PAC learner to infer the system and establish the sample complexity. Lastly, we present a formal analysis of the expressive power of the hypothesis class of dynamical systems where both the topology and behavior are unknown, using the well-known Natarajan dimension formalism. Our results provide a theoretical foundation for learning both the topology and behavior of discrete dynamical systems.

Evacuation planning is an essential part of disaster management where the goal is to relocate people under imminent danger to safety. However, finding jointly optimal evacuation routes and a schedule that minimizes the average evacuation time or evacuation completion time, is a computationally hard problem. As a result, large-scale evacuation routing and scheduling continues to be a challenge. In this paper, we present a game-theoretic approach to tackle this problem. We start by formulating a strategic routing and scheduling game, named the Evacuation Game: Routing and Scheduling (EGRES), where players choose their route and time of departure. We show that: (i) every instance of EGRES has at least one pure strategy Nash equilibrium, and (ii) an optimal outcome in an instance will always be an equilibrium in that instance. We then provide bounds on how bad an equilibrium can be compared to an optimal outcome. Additionally, we present a polynomial-time algorithm, the Sequential Action Algorithm (SAA), for finding equilibria in a given instance under a special condition. We use Virginia Beach City in Virginia, and Harris County in Houston, Texas as study areas and construct two EGRES instances. Our results show that, by utilizing SAA, we can efficiently find equilibria in these instances that have social objective close to the optimal value.

Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined communities (or clusters). Connections between pairs of vertices are generated randomly and independently with pre-defined probabilities, which depend on the communities containing the two nodes. A fundamental problem in SBMs is the recovery of the community structure, and sharp information-theoretic bounds are known for recoverability for many versions of SBMs. Our focus here is the recoverability problem in SBMs when the network is private. Under the edge differential privacy model, we derive conditions for exact recoverability in three different versions of SBMs, namely Asymmetric SBM (when communities have non-uniform sizes), General Structure SBM (with outliers), and Censored SBM (with edge features). Our private algorithms have polynomial running time w.r.t. the input graph’s size, and match the recovery thresholds of the non-private setting when $\epsilon\rightarrow\infty$. In contrast, the previous best results for recoverability in SBMs only hold for the symmetric case (equal size communities), and run in quasi-polynomial time, or in polynomial time with recovery thresholds being tight up to some constants from the non-private settings.

Networked dynamical systems are widely used as formal models of real-world cascading phenomena, such as the spread of diseases and information. Prior research has addressed the problem of learning the behavior of an unknown dynamical system when the underlying network has a single layer. In this work, we study the learnability of dynamical systems over multilayer networks, which are more realistic and challenging. First, we present an efficient PAC learning algorithm with provable guarantees to show that the learner only requires a small number of training examples to infer an unknown system. We further provide a tight analysis of the Natarajan dimension which measures the model complexity. Asymptotically, our bound on the Nararajan dimension is tight for almost all multilayer graphs. The techniques and insights from our work provide the theoretical foundations for future investigations of learning problems for multilayer dynamical systems.

While the worst of COVID-19 pandemic has most likely passed us, an occurrence of equally devastating global pandemic or regional epidemic cannot be ruled out in future. H1N1, Zika, SARS, MERS, and Ebola outbreaks over the past few decades have sharply illustrated our enormous vulnerability to emerging infectious diseases. While the data mining research community has demonstrated increased interest in epidemiological applications, much is still left to be desired. For example, there is an urgent need to develop sound theoretical principles and transformative computational approaches that will allow us to address the escalating threat of current and future pandemics. Data mining and knowledge discovery have an important role to play in this regard. Different aspects of infectious disease modeling, analysis, and control have traditionally been studied within the confines of individual disciplines, such as mathematical epidemiology and public health, and data mining and machine learning. Coupled with increasing data generation across multiple domains/sources (e.g., wastewater surveillance, electronic medical records, and social media), there is a clear need for analyzing them to inform public health policies and outcomes timely. Recent advances in disease surveillance and forecasting, and initiatives such as the CDC Flu Challenge, CDC COVID-19 Forecasting Hub etc., have brought these disciplines closer together. On the one hand, public health practitioners seek to use novel datasets, such as Safegraph, Unacast, and Google mobility data, and techniques like Graph Neural Networks. On the other hand, researchers from data mining and machine learning develop novel tools for solving many fundamental problems in the public health policy planning and decision-making process, leveraging novel datasets (e.g., COVID-19 behavioral health surveys, contact tracing trees, and satellite images of urban streets) and combining them with more traditional time series information (e.g., surveillance, hospitalization, and death records). We believe the next stage of advances will result from closer collaborations between these two groups, which is the main objective of epiDAMIK.

Heterogeneous agent-based models (HABMs) can simulate the dynamics of multiple types of entities and their interactions on contact networks. In recent years, they have gathered great interest and are widely applied in multiple fields, such as personalized recommendations, publication ranking, and epidemic modeling. Nevertheless, conventional HABMs on graphs can only capture pair-wise interactions between agents but fail to capture the more complex dynamics of group interactions (e.g., multiple people in the same location simultaneously), consequently leading to suboptimal performance. To address this, we propose using hypergraphs to capture such group interactions better and extend the current graph-based HABMs to hypergraphs. Specifically, we use MRSA (Methicillin-resistant Staphylococcus aureus, a kind of infectious disease acquired by patients during treatment at healthcare facilities) spread in the University of Virginia hospital as an example to showcase how we extend an existing graph-based HABM, Graph-HeterSIS, to a hypergraph-based HABM (H2ABM), Hypergraph-HeterSIS. We show how the hyper-graphs can capture the structural difference between contacts before and during the first wave of COVID-19 outbreak in Virginia better than graphs. Our experiments show that H2ABM better captures the underlying group interactions and better fits and forecasts MRSA cases.

Healthcare acquired infections (HAIs) (e.g., Methicillin-resistant Staphylococcus aureus infection) have complex transmission pathways, spreading not just via direct person-to-person contacts, but also via contaminated surfaces. Prior work in mathematical epidemiology has led to a class of models – which we call load sharing models – that provide a discrete-time, stochastic formalization of HAI-spread on temporal contact networks. The focus of this paper is the source detection problem for the load sharing model. The source detection problem has been studied extensively in SEIR type models, but this prior work does not apply to load sharing models. We show that a natural formulation of the source detection problem for the load sharing model is computationally hard, even to approximate. We then present two alternate formulations that are much more tractable. The tractability of our problems depends crucially on the submodularity of the expected number of infections as a function of the source set. Prior techniques for showing submodularity, such as the "live graph" technique are not applicable for the load sharing model and our key technical contribution is to use a more sophisticated "coupling" technique to show the submodularity result. We propose algorithms for our two problem formulations by extending existing algorithmic results from submodular optimization and combining these with an expectation propagation heuristic for the load sharing model that leads to orders-of-magnitude speedup. We present experimental results on temporal contact networks based on fine-grained EMR data from three different hospitals. Our results on synthetic outbreaks on these networks show that our algorithms outperform baselines by up to 5.97 times. Furthermore, case studies based on hospital outbreaks of Clostridioides difficile infection show that our algorithms identify clinically meaningful sources.

Only a subset of infections is actually observed in an outbreak, due to multiple reasons such as asymptomatic cases and under-reporting. Therefore, reconstructing an epidemic cascade given some observed cases is an important step in responding to such an outbreak. A maximum likelihood solution to this problem ( referred to as CascadeMLE ) can be shown to be a variation of the classical Steiner subgraph problem, which connects a subset of observed infections. In contrast to prior works on epidemic reconstruction, which consider the standard Steiner tree objective, we show that a solution to CascadeMLE, based on the actual MLE objective, has a very different structure. We design a logarithmic approximation algorithm for CascadeMLE, and evaluate it on multiple synthetic and social contact networks, including a contact network constructed for a hospital. Our algorithm has significantly better performance compared to a prior baseline.

Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. Two key problems concerning evolutionary games are the existence of a pure Nash equilibrium (NE) and the convergence time. In this work, we study these two problems for anti-coordination games under sequential and synchronous update schemes. For each update scheme, we examine two decision modes based on whether an agent considers its own previous action (self essential) or not (self non-essential) in choosing its next action. Using a relationship between games and dynamical systems, we show that for both update schemes, finding an NE can be done efficiently under the self non-essential mode but is computationally intractable under the self essential mode. We then identify special cases for which an NE can be obtained efficiently. For convergence time, we show that the dynamics converges in a polynomial number of steps under the synchronous scheme; for the sequential scheme, the convergence time is polynomial only under the self non-essential mode. Through experiments, we empirically examine the convergence time and the equilibria for both synthetic and real-world networks.

Vaccines have proven to be extremely effective in preventing the spread of COVID-19 and potentially ending the pandemic. Lack of access caused many people not getting vaccinated early, so states such as Virginia deployed mobile vaccination sites in order to distribute vaccines across the state. Here we study the problem of deciding where these facilities should be placed and moved over time in order to minimize the distance each person needs to travel in order to be vaccinated. Traditional facility location models for this problem fail to incorporate the fact that our facilities are mobile (i.e., they can move over time). To this end, we instead model vaccine distribution as the Dynamic k-Supplier problem and give the first approximation algorithms for this problem. We then run extensive simulations on real world datasets to show the efficacy of our methods. In particular, we find that natural baselines for Dynamic k-Supplier cannot take advantage of the mobility of the facilities, and perform worse than non-mobile k-Supplier algorithms.

Evacuation planning is a crucial part of disaster management. However, joint optimization of its two essential components, routing and scheduling, with objectives such as minimizing average evacuation time or evacuation completion time, is a computationally hard problem. To approach it, we present MIP-LNS, a scalable optimization method that utilizes heuristic search with mathematical optimization and can optimize a variety of objective functions. We also present the method MIP-LNS-SIM, where we combine agent-based simulation with MIP-LNS to estimate delays due to congestion, as well as, find optimized plans considering such delays. We use Harris County in Houston, Texas, as our study area. We show that, within a given time limit, MIP-LNS finds better solutions than existing methods in terms of three different metrics. However, when congestion dependent delay is considered, MIP-LNS-SIM outperforms MIP-LNS in multiple performance metrics. In addition, MIP-LNS-SIM has a significantly lower percent error in estimated evacuation completion time compared to MIP-LNS.

Set Cover is a fundamental problem in combinatorial optimization which has been studied for many decades due to its various applications across multiple domains. In many of these domains, the input data consists of locations, relationships, and other sensitive information of individuals which may leaked due to the set cover output. Attempts have been made to design privacy-preserving algorithms to solve the Set Cover under privacy constraints. Under differential privacy, it has been proved that the Set Cover problem has strong impossibility results and no explicit forms of the output can be released to the public. In this work, we observe that these hardness results dissolve when we turn to the Partial Set Cover problem, where we only need to cover a ρ ∈ (0,1) fraction of the elements. We show that this relaxation enables us to avoid the impossibility results, and give the first algorithm which outputs an explicit form of set cover with non-trivial utility guarantees under differential privacy. Using our algorithm as a subroutine, we design a differentially private bicriteria algorithm to solve a recently proposed facility location problem for vaccine distribution which generalizes the k-supplier with outliers. Our analysis shows that relaxing the covering requirement to serve only a ρ ∈ (0,1) fraction of the population/universe also allows us to circumvent the inherent hardness of k-supplier and give the first non-trivial guarantees.

The epiDAMIK workshop serves as a platform for advancing the utilization of data-driven methods in the fields of epidemiology and public health research. These fields have seen relatively limited exploration of data-driven approaches compared to other disciplines. Therefore, our primary objective is to foster the growth and recognition of the emerging discipline of data-driven and computational epidemiology, providing a valuable avenue for sharing state-of-the-art research and ongoing projects. The workshop also seeks to showcase results that are not typically presented at major computing conferences, including valuable insights gained from practical experiences. Our target audience encompasses researchers in AI, machine learning, and data science from both academia and industry, who have a keen interest in applying their work to epidemiological and public health contexts. Additionally, we welcome practitioners from mathematical epidemiology and public health, as their expertise and contributions greatly enrich the discussions. Homepage: https://epidamik.github.io/

We consider the setting of cascades that result from contagion dynamics on large realistic contact networks. We address the question of whether the structural properties of a (partially) observed cascade can characterize the contagion scenario and identify the interventions that might be in effect. Using epidemic spread as a concrete example, we study how social interventions such as compliance in social distancing, extent (and efficacy) of vaccination, and the transmissibility of disease can be inferred. The techniques developed are more generally applicable to other contagions as well.

Methicillin-resistant Staphylococcus aureus (MRSA) is a type of bacteria resistant to certain antibiotics, making it difficult to prevent MRSA infections. Among decades of efforts to conquer infectious diseases caused by MRSA, many studies have been proposed to estimate the causal effects of close contact (treatment) on MRSA infection (outcome) from observational data. In this problem, the treatment assignment mechanism plays a key role as it determines the patterns of missing counterfactuals --- the fundamental challenge of causal effect estimation. Most existing observational studies for causal effect learning assume that the treatment is assigned individually for each unit. However, on many occasions, the treatments are pairwisely assigned for units that are connected in graphs, i.e., the treatments of different units are entangled. Neglecting the entangled treatments can impede the causal effect estimation. In this paper, we study the problem of causal effect estimation with treatment entangled in a graph. Despite a few explorations for entangled treatments, this problem still remains challenging due to the following challenges: (1) the entanglement brings difficulties in modeling and leveraging the unknown treatment assignment mechanism; (2) there may exist hidden confounders which lead to confounding biases in causal effect estimation; (3) the observational data is often time-varying. To tackle these challenges, we propose a novel method NEAT, which explicitly leverages the graph structure to model the treatment assignment mechanism, and mitigates confounding biases based on the treatment assignment modeling. We also extend our method into a dynamic setting to handle time-varying observational data. Experiments on both synthetic datasets and a real-world MRSA dataset validate the effectiveness of the proposed method, and provide insights for future applications.

One of the most common problems studied in the context of differential privacy for graph data is counting the number of non-induced embeddings of a subgraph in a given graph. These counts have very high global sensitivity. Therefore, adding noise based on powerful alternative techniques, such as smooth sensitivity and higher-order local sensitivity have been shown to give significantly better accuracy. However, all these alternatives to global sensitivity become computationally very expensive, and to date efficient polynomial time algorithms are known only for few selected subgraphs, such as triangles, $k$-triangles, and $k$-stars. In this paper, we show that good approximations to these sensitivity metrics can be still used to get private algorithms. Using this approach, we much faster algorithms for privately counting the number of triangles in real-world social networks, which can be easily parallelized. We also give a private polynomial time algorithm for counting any constant size subgraph using less noise than the global sensitivity; we show this can be improved significantly for counting paths in special classes of graphs.

The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely adversarial or always equally prefers the positive label. In this paper, we generalize both of these through a unified framework by considering strategic agents with heterogenous preferences, and introduce the notion of strategic VC-dimension (SVC) to capture the PAC-learnability in our general strategic setup. SVC provably generalizes the recent concept of adversarial VC-dimension (AVC) introduced by Cullina et al. (2018). We instantiate our framework for the fundamental strategic linear classification problem. We fully characterize: (1) the statistical learnability of linear classifiers by pinning down its SVC; (2) its computational tractability by pinning down the complexity of the empirical risk minimization problem. Interestingly, the SVC of linear classifiers is always upper bounded by its standard VC-dimension. This characterization also strictly generalizes the AVC bound for linear classifiers in (Cullina et al., 2018). Finally, we briefly investigate the power of randomization in our strategic classification setup. We show that randomization may strictly increase the accuracy in general, but will not help in the special case of adversarial classification with zero-manipulation-cost.

The efficient detection of outbreaks and other cascading phenomena is a fundamental problem in a number of domains, including disease spread, social networks, and infrastructure networks. In such settings, monitoring and testing a small group of pre-selected nodes from the susceptible population (i.e., a sensor set) is often the preferred testing regime. We study the problem of selecting a sensor set that minimizes the delay in detection---we refer to this as the MinDelSS problem. Prior methods for minimizing the detection time rely on greedy algorithms using submodularity. We show that this approach can sometimes lead to a worse approximation for minimizing the detection time than desired. We also show that MinDelSS is hard to approximate within an O(n^(1-1/g))-factor for any constant g greater than or equal to 2 for a graph with n nodes. This instead motivates seeking a bicriteria approximations. We present the algorithm RoundSensor, which gives a rigorous worst case O(log(n))-factor for the detection time, while violating the budget by a factor of O(log^2(n)). Our algorithm is based on the sample average approximation technique from stochastic optimization, combined with linear programming and rounding. We evaluate our algorithm on several networks, including hospital contact networks, which validates its effectiveness in real settings.

Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the dissemination of undesirable contagions (such as rumors and misinformation), convergence to fixed points with a small number of affected nodes is a desirable goal. Motivated by such considerations, we formulate a novel optimization problem of finding a nontrivial fixed point of the system with the minimum number of affected nodes. We establish that, unless P = NP, there is no polynomial-time algorithm for approximating a solution to this problem to within the factor n^(1 - epsilon) for any constant epsilon > 0. To cope with this computational intractability, we identify several special cases for which the problem can be solved efficiently. Further, we introduce an integer linear program to address the problem for networks of reasonable sizes. For solving the problem on larger networks, we propose a general heuristic framework along with greedy selection methods. Extensive experimental results on real-world networks demonstrate the effectiveness of the proposed heuristics. A full version of the manuscript, source code and data are available at: https://github.com/bridgelessqiu/NMIN-FPE

The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinInfEdge problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most B edges; similarly the MinInfNode problem involves removing at most B vertices. These are fundamental problems in epidemiology and network science. While a number of heuristics have been considered, the complexity of this problem remains generally open. In this paper, we present two bicriteria approximation algorithms for the MinInfEdge problem, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result technique of Karger, which works for any graph, when the transmission probabilities are not too small. The second is a Sample Average Approximation (SAA) based algorithm, which we analyze for the Chung-Lu random graph model. We also extend some of our results for the MinInfNode problem.

Graph cut problems are fundamental in combinatorial Optimization, and are a central object of study in both theory and practice. Further, the study of fairness in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed for a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different notions of fairness, namely demographic and probabilistic individual fairness, in a particular cut problem that models disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.

Synthetic data is gaining rapid importance in many application domains due to privacy issues, bias, lack, or simply unavailability of real data. It is important that the synthetic data be a good representation of real data for successfully completing the task at hand. Thus, devising characteristic validation metrics is crucial and remains an open problem in many domains (e.g., image generation). Good validation metrics must be able to disentangle the differences between the quality and the variability coverage of the synthetic data. We propose to use a 3-dimensional metric (precision α, recall β, coverage γ) to describe the fidelity and diversity of the synthetic data. In this paper, we improve on existing definitions of precision, recall, and coverage to extend to large scale time series data. Traditional nearest neighbor manifolds from the literature are replaced by unsupervised learning techniques such as clustering to deal with large scale fine resolution time series while computing the validation metrics. The proposed metrics are employed to validate synthetic data in the domain of residential energy demand. In addition, we extend these definitions to datasets that have a natural hierarchical structure. We propose a hierarchical data-tree model in which precision, recall, and coverage can be computed at multiple inherent (and/or custom) levels of groupings of the data.

Evacuation planning is an essential part of disaster management where the goal is to relocate people in a safe and orderly manner. Existing research has shown that such problems are hard to approximate and current methods are difficult to scale to real-life applications. We introduce a notion of fairness and two related objectives while studying evacuation planning, namely: minimizing maximum inconvenience and minimizing average inconvenience. We show that both problems are not just NP-hard to solve exactly, but in fact are NP-hard to approximate. On the positive side, we present a heuristic optimization method MIP-LNS, based on the well-known Large Neighborhood Search framework, that can find good approximate solutions in reasonable amount of time. We also consider a multi-objective problem where the goal is to minimize both objectives and solve it using MIP-LNS. We use real-world road network and population data from Harris County in Houston, Texas (a region that needed large-scale evacuations in the past), and apply MIP-LNS to calculate evacuation plans for the area. We compare the quality of the plans in terms of evacuation efficiency and fairness. We find that the solutions to the multi-objective problem are superior in both of these aspects. We also perform statistical tests to show that the solutions are significantly different.

The goal of community detection over graphs is to recover underlying labels/attributes of users (e.g., political affiliation) given the connectivity between users. There has been significant recent progress on understanding the fundamental limits of community detection when the graph is generated from a stochastic block model (SBM). Specifically, sharp information theoretic limits and efficient algorithms have been obtained for SBMs as a function of $p$ and $q$, which represent the intra-community and inter-community connection probabilities. In this paper, we study the community detection problem while preserving the privacy of the individual connections between the vertices. Focusing on the notion of $(\epsilon, \delta)$-edge differential privacy (DP), we seek to understand the fundamental tradeoffs between $(p, q)$, DP budget $(\epsilon, \delta)$, and computational efficiency for exact recovery of community labels. To this end, we present and analyze the associated information-theoretic tradeoffs for three differentially private community recovery mechanisms: a) stability based mechanism; b) sampling based mechanisms; and c) graph perturbation mechanisms. Our main findings are that stability and sampling based mechanisms lead to a superior tradeoff between $(p,q)$ and the privacy budget $(\epsilon, \delta)$; however this comes at the expense of higher computational complexity. On the other hand, albeit low complexity, graph perturbation mechanisms require the privacy budget $\epsilon$ to scale as $\Omega(\log(n))$ for exact recovery.

Using a discrete dynamical system model, many papers have addressed the problem of learning the behavior (i.e., the local function at each node) of a networked system through active queries, assuming that the network topology is known. We address the problem of inferring both the topology of the network and the behavior of a discrete dynamical system through active queries. We consider two query models studied in the literature, namely the batch model (where all the queries must be submitted together) and the adaptive model (where responses to previous queries can be used in formulating a new query). Our results are for systems where the state of each node is from {0,1} and the local functions are Boolean. We present algorithms to learn the topology and the behavior under both batch and adaptive query models for several classes of dynamical systems. These algorithms use only a polynomial number of queries. We also present experimental results obtained by running our query generation algorithms on synthetic and real-world networks.

Residential consumers have become active participants in the power distribution network after being equipped with residential EV charging provisions. This creates a challenge for the network operator tasked with dispatching electric power to the residential consumers through the existing distribution network infrastructure in a reliable manner. In this paper, we address the problem of scheduling residential EV charging for multiple consumers while maintaining network reliability. An additional challenge is the restricted exchange of information: where the consumers do not have access to network information and the network operator does not have access to consumer load parameters. We propose a distributed framework which generates an optimal EV charging schedule for individual residential consumers based on their preferences and iteratively updates it until the network reliability constraints set by the operator are satisfied. We validate the proposed approach for different EV adoption levels in a synthetically created digital twin of an actual power distribution network. The results demonstrate that the new approach can achieve a higher level of network reliability compared to the case where residential consumers charge EVs based solely on their individual preferences, thus providing a solution for the existing grid to keep up with increased adoption rates without significant investments in increasing grid capacity.

We study the problem of designing scalable algorithms to find effective intervention strategies for controlling stochastic epidemic processes on networks. This is a common problem arising in agent based models for epidemic spread. Previous approaches to this problem focus on either heuristics with no guarantees or approximation algorithms that scale only to networks corresponding to county-sized populations, typically, with less than a million nodes. In particular, the mathematical-programming based approaches need to solve the Linear Program (LP) relaxation of the problem using an LP solver, which restricts the scalability of this approach. In this work, we overcome this restriction by designing an algorithm that adapts the multiplicative weights update (MWU) framework, along with the sample average approximation (SAA) technique, to approximately solve the linear program (LP) relaxation for the problem. To scale this approach further, we provide a memory-efficient algorithm that enables scaling to large networks, corresponding to country-size populations, with over 300 million nodes and 30 billion edges. Furthermore, we show that this approach provides near-optimal solutions to the LP in practice.

Similar to previous iterations, the epiDAMIK @ KDD workshop is a forum to promote data driven approaches in epidemiology and public health research. Even after the devastating impact of COVID-19 pandemic, data driven approaches are not as widely studied in epidemiology, as they are in other spaces. We aim to promote and raise the profile of the emerging research area of data-driven and computational epidemiology, and create a venue for presenting state-of-the-art and in-progress results-in particular, results that would otherwise be difficult to present at a major data mining conference, including lessons learnt in the 'trenches'. The current COVID-19 pandemic has only showcased the urgency and importance of this area. Our target audience consists of data mining and machine learning researchers from both academia and industry who are interested in epidemiological and public-health applications of their work, and practitioners from the areas of mathematical epidemiology and public health. Homepage: https://epidamik.github.io/.

We study allocation of COVID-19 vaccines to individuals based on the structural properties of their underlying social contact network. Using a realistic representation of a social contact network for the Commonwealth of Virginia, we study how a limited number of vaccine doses can be strategically distributed to individuals to reduce the overall burden of the pandemic. We show that allocation of vaccines based on individuals' degree (number of social contacts) and total social proximity time is significantly more effective than the usually used age-based allocation strategy in reducing the number of infections, hospitalizations and deaths. The overall strategy is robust even: (i) if the social contacts are not estimated correctly; (ii) if the vaccine efficacy is lower than expected or only a single dose is given; (iii) if there is a delay in vaccine production and deployment; and (iv) whether or not non-pharmaceutical interventions continue as vaccines are deployed. For reasons of implementability, we have used degree, which is a simple structural measure and can be easily estimated using several methods, including the digital technology available today. These results are significant, especially for resource-poor countries, where vaccines are less available, have lower efficacy, and are more slowly distributed.

Vaccination is the primary intervention for controlling the spread of infectious diseases. A certain level of vaccination rate (referred to as "herd immunity") is needed for this intervention to be effective. However, there are concerns that herd immunity might not be achieved due to an increasing level of hesitancy and opposition to vaccines. One of the primary reasons for this is the cost of non-conformance with one's peers. We use the framework of network coordination games to study the persistence of anti-vaccine sentiment in a population. We extend it to incorporate the opposing forces of the pressure of conforming to peers, herd-immunity and vaccination benefits. We study the structure of the equilibria in such games, and the characteristics of unvaccinated nodes. We also study Stackelberg strategies to reduce the number of nodes with anti-vaccine sentiment. Finally, we evaluate our results on different kinds of real world social networks.

The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. We also explore a number of variants where additional constraints are imposed on the first-stage decisions, specifically matroid and multi-knapsack constraints. Our eventual goal is to provide results for supplier problems in the most general distributional setting, where there is only black-box access to the underlying distribution. To that end, we follow a two-step approach. First, we develop algorithms for a restricted version of each problem, in which all possible scenarios are explicitly provided; second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we crucially exploit properties of the restricted-case algorithms. We finally note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.

We study the role of vaccine acceptance in controlling the spread of COVID-19 in the US using AI-driven agent-based models. Our study uses a 288 million node social contact network spanning all 50 US states plus Washington DC, comprised of 3300 counties, with 12.59 billion daily interactions. The highly-resolved agent-based models use realistic information about disease progression, vaccine uptake, production schedules, acceptance trends, prevalence, and social distancing guidelines. Developing a national model at this resolution that is driven by realistic data requires a complex scalable workflow, model calibration, simulation, and analytics components. Our workflow optimizes the total execution time and helps in improving overall human productivity.This work develops a pipeline that can execute US-scale models and associated workflows that typically present significant big data challenges. Our results show that, when compared to faster and accelerating vaccinations, slower vaccination rates due to vaccine hesitancy cause averted infections to drop from 6.7M to 4.5M, and averted total deaths to drop from 39.4K to 28.2K nationwide. This occurs despite the fact that the final vaccine coverage is the same in both scenarios. Improving vaccine acceptance by 10% in all states increases averted infections from 4.5M to 4.7M (a 4.4% improvement) and total deaths from 28.2K to 29.9K (a 6% increase) nationwide. The analysis also reveals interesting spatio-temporal differences in COVID-19 dynamics as a result of vaccine acceptance. To our knowledge, this is the first national-scale analysis of the effect of vaccine acceptance on the spread of COVID-19, using detailed and realistic agent-based models.

Densest subgraph detection is a fundamental graph mining problem, with a large number of applications. There has been a lot of work on efficient algorithms for finding the densest subgraph in massive networks. However, in many domains, the network is private, and returning a densest subgraph can reveal information about the network. Differential privacy is a powerful framework to handle such settings. We study the densest subgraph problem in the edge privacy model, in which the edges of the graph are private. We present the first sequential and parallel differentially private algorithms for this problem. We show that our algorithms have an additive approximation guarantee. We evaluate our algorithms on a large number of real-world networks, and observe a good privacy-accuracy tradeoff when the network has high density.

The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely adversarial or always equally prefers the positive label. In this paper, we generalize both of these through a unified framework for strategic classification and introduce the notion of strategic VC-dimension (SVC) to capture the PAC-learnability in our general strategic setup. SVC provably generalizes the recent concept of adversarial VC-dimension (AVC) introduced by Cullina et al. (2018). We instantiate our framework for the fundamental strategic linear classification problem. We fully characterize: (1) the statistical learnability of linear classifiers by pinning down its SVC; (2) it’s computational tractability by pinning down the complexity of the empirical risk minimization problem. Interestingly, the SVC of linear classifiers is always upper bounded by its standard VC-dimension. This characterization also strictly generalizes the AVC bound for linear classifiers in (Cullina et al., 2018).

The 4th [email protected] workshop is a forum to discuss new insights into how data mining can play a bigger role in epidemiology and public health research. While the integration of data science methods into epidemiology has significant potential, it remains under studied. We aim to raise the profile of this emerging research area of data-driven and computational epidemiology, and create a venue for presenting state-of-the-art and in-progress results-in particular, results that would otherwise be difficult to present at a major data mining conference, including lessons learnt in the 'trenches'. The current COVID-19 pandemic has only showcased the urgency and importance of this area. Our target audience consists of data mining and machine learning researchers from both academia and industry who are interested in epidemiological and public-health applications of their work, and practitioners from the areas of mathematical epidemiology and public health.

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS 2018] for constructing succinct representations for clusters. Given a set of objects S, a partition π of S (into clusters), and a universe T of tags such that each element in S is associated with a subset of tags, the goal is to find a representative set of tags for each cluster such that those sets are pairwise-disjoint and the total size of all the representatives is minimized. Since this problem is NP-hard in general, we develop approximation algorithms with provable performance guarantees for the problem. We also show applications to explain clusters from datasets, including clusters of genomic sequences that represent different threat levels.

The well-studied influence maximization problem involves choosing a seed set of a given size, which maximizes the expected influence. However, such solutions might have a significant probability of achieving low influence, which might not be suitable in many applications. In this paper, we consider a different approach: find a seed set that maximizes the influence set size with a given probability. We show that this objective is not submodular, and design a greedy, multi-criteria approximation algorithm for this problem with rigorous approximation guarantees. We also evaluate our algorithm on multiple datasets, and show that they have similar or better quality as the ones optimizing the expected influence, but with additional guarantees on the probability.

Evacuation planning methods aim to design routes and schedules to relocate people to safety in the event of natural or man-made disasters. The primary goal is to minimize casualties which often requires the evacuation process to be completed as soon as possible. In this paper, we present QueST, an agent-based discrete event queuing network simulation system, and STEERS, an iterative routing algorithm that uses QueST for designing and evaluating large scale evacuation plans in terms of total egress time and congestion/bottlenecks occurring during evacuation. We use the Houston Metropolitan Area, which consists of nine US counties and spans an area of 9,444 square miles as a case study, and compare the performance of STEERS with two existing route planning methods. We find that STEERS is either better or comparable to these methods in terms of total evacuation time and congestion faced by the evacuees. We also analyze the large volume of data generated by the simulation process to gain insights about the scenarios arising from following the evacuation routes prescribed by these methods.

It is well known that physical interdependencies exist between networked civil infrastructures such as transportation and power system networks. In order to analyze complex nonlinear correlations between such networks, datasets pertaining to such real infrastructures are required. However, such data are not readily available due to their proprietary nature. This work proposes a methodology to generate realistic synthetic power distribution networks for a given geographical region. A network generated in this manner is not the actual distribution system, but its functionality is very similar to the real distribution network. The synthetic network connects high voltage substations to individual residential consumers through primary and secondary distribution networks. Here, the distribution network is generated by solving an optimization problem which minimizes the overall length of the network subject to structural and power flow constraints. This work also incorporates identification of long high voltage feeders originating from substations and connecting remotely situated customers in rural geographic locations while maintaining voltage regulation within acceptable limits. The proposed methodology is applied to the state of Virginia and creates synthetic distribution networks which are validated by comparing them to actual power distribution networks at the same location.

Can we infer all the failed components of an infrastructure network, given a sample of reachable nodes from supply nodes? One of the most critical post-disruption processes after a natural disaster is to quickly determine the damage or failure states of critical infrastructure components. However, this is nontrivial, considering that often only a fraction of components may be accessible or observable after a disruptive event. Past work has looked into inferring failed components given point probes, i.e. with a direct sample of failed components. In contrast, we study the harder problem of inferring failed components given partial information of some `serviceable' reachable nodes and a small sample of point probes, being the first often more practical to obtain. We formulate this novel problem using the Minimum Description Length (MDL) principle, and then present a greedy algorithm that minimizes MDL cost effectively. We evaluate our algorithm on domain-expert simulations of real networks in the aftermath of an earthquake. Our algorithm successfully identifies failed components, especially the critical ones affecting the overall system performance.

Preventing and slowing the spread of epidemics is achieved through techniques such as vaccination and social distancing. Given practical limitations on the number of vaccines and cost of administration, optimization becomes a necessity. Previous approaches using mathematical programming methods have shown to be effective but are limited by computational costs. In this work, we present PREEMPT, a new approach for intervention via maximizing the influence of vaccinated nodes on the network. We prove submodular properties associated with the objective function of our method so that it aids in construction of an efficient greedy approximation strategy. Consequently, we present a new parallel algorithm based on greedy hill climbing for PREEMPT, and present an efficient parallel implementation for distributed CPU-GPU heterogeneous platforms. Our results demonstrate that PREEMPT is able to achieve a significant reduction (up to 6.75×) in the percentage of people infected and up to 98% reduction in the peak of the infection on a city-scale network. We also show strong scaling results of PREEMPT on up to 128 nodes of the Summit supercomputer. Our parallel implementation is able to significantly reduce time to solution, from hours to minutes on large networks. This work represents a first-of-its-kind effort in parallelizing greedy hill climbing and applying it toward devising effective interventions for epidemics.

Subgraph counting aims to count occurrences of a template T in a given network G (V, E). It is a powerful graph analysis tool and has found real-world applications in diverse domains. Scaling subgraph counting problems is known to be memory bounded and computationally challenging with exponential complexity. Although scalable parallel algorithms are known for several graph problems such as Triangle Counting and PageRank, this is not common for counting complex subgraphs. Here we address this challenge and study connected acyclic graphs or trees. We propose a novel vectorized subgraph counting algorithm, named SUBGRAPH2VEC, as well as both shared memory and distributed implementations: 1) reducing algorithmic complexity by minimizing neighbor traversal; 2) achieving a highly-vectorized implementation upon linear algebra kernels to significantly improve performance and hardware utilization. 3) SUBGRAPH2VEC improves the overall performance over the state-of-the-art work by orders of magnitude and up to 660x on a single node. 4) SUBGRAPH2VEC in distributed mode can scale up the template size to 20 and maintain good strong scalability. 5) enabling portability to both CPU and GPU.

We consider the PAC learnability of the local functions at the vertices of a discrete networked dynamical system, assuming that the underlying network is known. Our focus is on the learnability of threshold functions. We show that several variants of threshold functions are PAC learnable and provide tight bounds on the sample complexity. In general, when the input consists of positive and negative examples, we show that the concept class of threshold functions is not efficiently PAC learnable, unless NP = RP. Using a dynamic programming approach, we show efficient PAC learnability when the number of negative examples is small. We also present an efficient learner which is consistent with all the positive examples and at least (1-1/e) fraction of the negative examples. This algorithm is based on maximizing a submodular function under matroid constraints. By performing experiments on both synthetic and real-world networks, we study how the network structure and sample complexity influence the quality of the inferred system.

According to the Centers for Disease Control and Prevention (CDC), one in twenty five hospital patients are infected with at least one healthcare acquired infection (HAI) on any given day. Early detection of possible HAI outbreaks help practitioners implement countermeasures before the infection spreads extensively. Here, we develop an efficient data and model driven method to detect outbreaks with high accuracy. We leverage mechanistic modeling of C. difficile infection, a major HAI disease, to simulate its spread in a hospital wing and design efficient near-optimal algorithms to select people and locations to monitor using an optimization formulation. Results show that our strategy detects up to 95% of "future" C. difficile outbreaks. We design our method by incorporating specific hospital practices (like swabbing for infections) as well. As a result, our method outperforms state-of-the-art algorithms for outbreak detection. Finally, a qualitative study of our result shows that the people and locations we select to monitor as sensors are intuitive and meaningful.

Prophylactic interventions such as vaccine allocation are some of the most effective public health policy planning tools. The supply of vaccines, however, is limited and an important challenge is to optimally allocate the vaccines to minimize epidemic impact. This resource allocation question (which we refer to as VaccIntDesign) has multiple dimensions: when, where, to whom, etc. Most of the existing literature in this topic deals with the latter (to whom), proposing policies that prioritize individuals by age and disease risk. However, since seasonal influenza spread has a typical spatial trend, and due to the temporal constraints enforced by the availability schedule, the when and where problems become equally, if not more, relevant. In this paper, we study the VaccIntDesign problem in the context of seasonal influenza spread in the United States. We develop a national scale metapopulation model for influenza that integrates both short and long distance human mobility, along with realistic data on vaccine uptake. We also design GreedyAlloc, a greedy algorithm for allocating the vaccine supply at the state level under temporal constraints and show that such a strategy improves over the current baseline of pro-rata allocation, and the improvement is more pronounced for higher vaccine efficacy and moderate flu season intensity. Further, the resulting strategy resembles a ring vaccination applied spatiallyacross the US.

One fundamental task in network analysis is detecting “hotspots” or “anomalies” in the network; that is, detecting subgraphs where there is significantly more activity than one would expect given historical data or some baseline process. Scan statistics is one popular approach used for anomalous subgraph detection. This methodology involves maximizing a score function over all connected subgraphs, which is a challenging computational problem. A number of heuristics have been proposed for these problems, but they do not provide any quality guarantees. Here, we propose a framework for designing algorithms for optimizing a large class of scan statistics for networks, subject to connectivity constraints. Our algorithms run in time that scales linearly on the size of the graph and depends on a parameter we call the “effective solution size,” while providing rigorous approximation guarantees. In contrast, most prior methods have super-linear running times in terms of graph size. Extensive empirical evidence demonstrates the effectiveness and efficiency of our proposed algorithms in comparison with state-of-the-art methods. Our approach improves on the performance relative to all prior methods, giving up to over 25% increase in the score. Further, our algorithms scale to networks with up to a million nodes, which is 1--2 orders of magnitude larger than all prior applications.

Scan statistics is one of the most popular approaches for anomaly detection in spatial and network data. In practice, there are numerous sources of uncertainty in the observed data. However, most prior works have overlooked such uncertainty, which can affect the accuracy and inferences of such methods. In this paper, we develop the first systematic approach to incorporating uncertainty in scan statistics. We study two formulations for robust scan statistics, one based on the sample average approximation and the other using a max-min objective. We show that uncertainty significantly increases the computational complexity of these problems. Rigorous algorithms and efficient heuristics for both formulations are developed with justification of theoretical bounds. We evaluate our proposed methods on synthetic and real datasets, and we observe that our methods give significant improvement in the detection power as well as optimization objective, relative to a baseline.

Anomaly detection is a fundamental problem in dynamic networks. In this paper, we study an approach for identifying anomalous subgraphs based on the Heaviest Dynamic Subgraph (HDS) problem. The HDS in a time-evolving edge-weighted graph consists of a pair containing a subgraph and subinterval whose sum of edge weights is maximized. The HDS problem in a static graph is equivalent to the Prize Collecting Steiner Tree (PCST) problem with the Net-Worth objective---this is a very challenging problem, in general, and numerous heuristics have been proposed. Prior methods for the HDS problem use the PCST solution as a heuristic, and run in time quadratic in the size of the graph. As a result, they do not scale well to large instances. In this paper, we develop a new approach for the HDS problem, which combines rigorous algorithmic and practical techniques and has much better scalability. Our algorithm is able to extend to other variations of the HDS problem, such as the problem of finding multiple anomalous regions. We evaluate our algorithms in a diverse set of real and synthetic networks, and we find solutions with higher score and better detection power for anomalous events compared to earlier heuristics.

We focus on two classes of problems in graph mining: (1) finding trees and (2) anomaly detection in complex networks using scan statistics. These are fundamental problems in a broad class of applications. Most of the parallel algorithms for such problems are either based on heuristics, which do not scale very well, or use techniques like color coding, which have a high memory overhead. In this paper, we develop a novel approach for parallelizing both these classes of problems, using an algebraic representation of subgraphs as monomials-this methodology involves detecting multilinear terms in multivariate polynomials. Our algorithms show good scaling over a large regime, and they run on networks with close to half one billion edges. The resulting parallel algorithm for trees is able to scale to subgraphs of size 18, which has not been done before, and it significantly outperforms the best prior color coding based method (FASCIA) by more than two orders of magnitude. Our algorithm for network scan statistics is the first such parallelization, and it is able to handle a broad class of scan statistics functions with the same approach.

In many applications, such as the Internet and infrastructure networks, nodes fail or get congested dynamically. We study the problem of inferring all the failed nodes, when only a sample of the failures is known, and there exist correlations between node failures/congestion in networks. We formalize this as the GraphStateInf problem, using the Minimum Description Length (MDL) principle. We propose the GraphMap algorithm for minimizing the MDL cost, and show that it gives an additive approximation, relative to the optimal. We evaluate our methods on synthetic and real datasets, which includes one from WAZE which gives traffic incident reports for the city of Boston. We find that our method gives promising results in recovering the missing failures.

BACKGROUND: Visualization plays an important role in epidemic time series analysis and forecasting. Viewing time series data plotted on a graph can help researchers identify anomalies and unexpected trends that could be overlooked if the data were reviewed in tabular form; these details can influence a researcher's recommended course of action or choice of simulation models. However, there are challenges in reviewing data sets from multiple data sources - data can be aggregated in different ways (e.g., incidence vs. cumulative), measure different criteria (e.g., infection counts, hospitalizations, and deaths), or represent different geographical scales (e.g., nation, HHS Regions, or states), which can make a direct comparison between time series difficult. In the face of an emerging epidemic, the ability to visualize time series from various sources and organizations and to reconcile these datasets based on different criteria could be key in developing accurate forecasts and identifying effective interventions. Many tools have been developed for visualizing temporal data; however, none yet supports all the functionality needed for easy collaborative visualization and analysis of epidemic data. RESULTS: In this paper, we present EpiViewer, a time series exploration dashboard where users can upload epidemiological time series data from a variety of sources and compare, organize, and track how data evolves as an epidemic progresses. EpiViewer provides an easy-to-use web interface for visualizing temporal datasets either as line charts or bar charts. The application provides enhanced features for visual analysis, such as hierarchical categorization, zooming, and filtering, to enable detailed inspection and comparison of multiple time series on a single canvas. Finally, EpiViewer provides several built-in statistical Epi-features to help users interpret the epidemiological curves. CONCLUSION: EpiViewer is a single page web application that provides a framework for exploring, comparing, and organizing temporal datasets. It offers a variety of features for convenient filtering and analysis of epicurves based on meta-attribute tagging. EpiViewer also provides a platform for sharing data between groups for better comparison and analysis. Our user study demonstrated that EpiViewer is easy to use and fills a particular niche in the toolspace for visualization and exploration of epidemiological data.

Detecting “hotspots” and “anomalies” is a recurring problem with a wide range of applications, such as social network analysis, epidemiology, finance, and biosurveillance, among others. Networks are a common abstraction in these applications for representing complex relationships. Typically, these networks are dynamic-, i.e., they evolve over time. A number of methods have been proposed for anomaly detection in such dynamic network data sets, which are primarily based on changes in network properties. We provide a survey of the various formulations of anomaly detection in dynamic networks with a focus on “window-based” methods. Window-based methods first define a time window of past network snapshots to model normal behavior and then mark a snapshot as anomalous if it has significantly different patterns from those observed in the time window. We describe two classes of techniques: 1) generalizations of Steiner connectivity; and 2) dense subgraph mining. Both have been used extensively in window-based graph anomaly detection. We summarize the key problem formulations that have been studied using these approaches, and we describe details of some of the main techniques.

Graph scan statistics have become popular for event detection in networks. This methodology involves finding connected subgraphs that maximize a certain anomaly function, but maximizing these functions is computationally hard in general. We develop a novel approach for graph scan statistics with connectivity constraints. Our algorithm Approx-MultilinearScan relies on an algebraic technique called multilinear detection, and it improves over prior methods for large networks. We also develop a Pregel-based parallel version of this algorithm in Giraph, MultilinearScanGiraph, that allows us to solve instances with over 40 million edges, which is more than one order of magnitude larger than existing methods.

Persistent and zero-day attacks have increased considerably in the recent past in terms of scale and impact. Security experts can no longer rely only on known defenses and thereby protect their resources permanently. It is increasingly common now to observe attackers being able to repeatedly break systems exploiting new vulnerabilities and defenders hardening systems with new measures. To model this phenomenon of the repeated takeover of the computing resources by system administrators and malicious attackers, a novel game framework, FlipIt, has been proposed by (Van Dijk et al. 2013) for a system consisting of a single resource. In this paper, we extend this and develop FlipNet, which is a repeated game framework for a networked system of multiple resources. This game involves two players-a defender and an attacker. Each player's objective is to maximize its gain (i.e., its control over the nodes in the network with stealthy moves), while minimizing the cost for making those moves. This leads to a novel and natural game formulation, with a very complex strategy space, that depends on the network structure. We show that finding the best response strategy for both the defender and attacker is NP-hard. In a key result in this study, we show that the attacker's gain for an instance of the game has a type of diminishing marginal return property, which leads to a near-optimal algorithm for maximizingthe attacker's gain. We examine the impact of network structure on the strategy space using simulations.

Given a contact network and coarse-grained diagnostic information like electronic Healthcare Reimbursement Claims (eHRC) data, can we develop efficient intervention policies to control an epidemic? Immunization is an important problem in multiple areas especially epidemiology and public health. However, most existing studies focus on developing pre-emptive strategies assuming prior epidemiological models. In practice, disease spread is usually complicated, hence assuming an underlying model may deviate from true spreading patterns, leading to possibly inaccurate interventions. Additionally, the abundance of health care surveillance data (like eHRC) makes it possible to study data-driven strategies without too many restrictive assumptions. Hence, such an approach can help public-health experts take more practical decisions. In this paper, we take into account propagation log and contact networks for controlling propagation. We formulate the novel and challenging Data-Driven Immunization problem without assuming classical epidemiological models. To solve it, we first propose an efficient sampling approach to align surveillance data with contact networks, then develop an efficient algorithm with the provably approximate guarantee for immunization. Finally, we show the effectiveness and scalability of our methods via extensive experiments on multiple datasets, and conduct case studies on nation-wide real medical surveillance data.

Scan statistics is a popular approach used for detecting “hotspots” and “anomalies” in spatio-temporal and network data. This methodology involves maximizing a score function over all connected subgraphs, which is NP-hard in general. A number of heuristics have been proposed for these problems, but they do not provide any quality guarantees. In this paper, we develop a framework for designing algorithms for optimizing a large class of scan statistics for networks, subject to connectivity constraints. Our algorithms run in time that scales linearly on the size of the graph and depends on a parameter we call the “effective solution size”, while providing rigorous approximation guarantees. In contrast, most prior methods have super-linear running times in terms of graph size. Extensive empirical evidence demonstrates the effectiveness and efficiency of our proposed algorithms in comparison with state-of-the-art methods. Our approach improves on the performance relative to all prior methods, giving up to over 25% increase in the score. Further, our algorithms scale to networks with up to a million nodes, which is 1–2 orders of magnitude larger than all prior applications.

The decision to take vaccinations and other protective interventions for avoiding an infection is a natural game-theoretic setting. Most of the work on vaccination games has focused on decisions at the start of an epidemic. However, a lot of people defer their vaccination decisions, in practice. For example, in the case of the seasonal flu, vaccination rates gradually increase, as the epidemic rate increases. This motivates the study of temporal vaccination games, in which vaccination decisions can be made more than once. An important issue in the context of temporal decisions is that of resource limitations, which may arise due to production and distribution constraints. While there has been some work on temporal vaccination games, resource constraints have not been considered. In this paper, we study temporal vaccination games for epidemics in the SI (susceptible-infectious) model, with resource constraints in the form of a repeated game in complex social networks, with budgets on the number of vaccines that can be taken at any time. We find that the resource constraints and the vaccination and infection costs have a significant impact on the structure of Nash equilibria (NE). In general, the budget constraints can cause NE to become very inefficient, and finding efficient NE as well as the social optimum are NP-hard problems. We develop algorithms for finding NE and approximating the social optimum. We evaluate our results using simulations on different kinds of networks.

Hospitals are typically optimized to operate near capacity, and there are serious concerns that our healthcare system is not prepared for the next pandemic. Stockpiles of different supplies, e.g., personal protective equipments (PPE) and medical equipment, need to be maintained in order to be able to respond to any future pandemics. Large outbreaks occur with a low probability, and such stockpiles require big investments. Further, hospitals often have mutual sharing agreements, which makes the problem of stockpiling decisions a natural game-theoretical problem. In this paper, we formalize hospital stockpiling as a game-theoretical problem. We use the notion of pairwise Nash stability as a solution concept for this problem, and characterize its structure. We show that stable strategies can lead to high unsatisfied demands in some scenarios, and stockpiles might not be maintained at all nodes. We also show that stable strategies and the social optimum can be computed efficiently.

Signed networks remain relatively under explored despite the fact that many real networks are of this kind. Here, we study the problem of subgraph density in signed networks and show connections to the event detection task. Notions of density have been used in prior studies on anomaly detection, but all existing methods have been developed for unsigned networks. We develop the first algorithms for finding dense subgraphs in signed networks using semi-definite programming based rounding. We give rigorous guarantees for our algorithms, and develop a heuristic EGOSCAN which is significantly faster. We evaluate the performance of EGOSCAN for different notions of density, and observe that it performs significantly better than natural adaptations of prior algorithms for unsigned networks. In particular, the improvement in edge density over previous methods is as much as 85% and usually over 50%. These results are consistent across signed and unsigned networks in different domains. The improvement in performance is even more significant for a constrained version of the problem involving finding subgraphs containing a subset of query nodes. We also develop an event detection method for signed and unsigned networks based on subgraph density. We apply this to three different temporal datasets, and show that our method based on EGOSCAN significantly outperforms existing approaches and baseline methods in terms of the precision-recall tradeoff (by as much as 25-50% in some instances).

Interventions such as vaccinations or installing anti-virus software are common strategies for controlling the spread of epidemics and malware on complex networks. Typically, nodes decide whether to implement such an intervention independently, depending on the costs they incur. A node can be protected by herd immunity, if enough other nodes implement such an intervention, making the problem of determining strategic decisions for vaccination a natural game-theoretical problem. There has been a lot of work on vaccination and network security game models, but all these models assume the vaccination decisions are made at the start of the game. However, in practice, a lot of individuals defer their vaccination decision, and the reasons for this behavior are not well understood, especially in network models. In this paper, we study a novel repeated game formulation, which considers vaccination decisions over time. We characterize Nash equilibria and the social optimum in such games, and find that a significant fraction of vaccinations might be deferred, in general. This depends crucially on the network structure, and the information and the vaccination delay. We show that finding Nash equilibria and the social optimum are NP-hard in general, and we develop an approximation algorithm for the social optimum whose approximation guarantee depends on the delay.

EMBERS is an anticipatory intelligence system forecasting population-level events in multiple countries of Latin America. A deployed system from 2012, EMBERS has been generating alerts 24x7 by ingesting a broad range of data sources including news, blogs, tweets, machine coded events,currency rates, and food prices. In this paper, we describe our experiences operating EMBERS continuously for nearly 4 years, with specific attention to the discoveries it has enabled, correct as well as missed forecasts, lessons learnt from participating in a forecasting tournament, and our perspectives on the limits of forecasting including ethical considerations.

Many real-world systems and networks are modeled and analyzed using various random graph models. These models must incorporate relevant properties such as degree distribution and clustering coefficient. Many models, such as the Chung-Lu (CL), stochastic Kronecker, stochastic block model (SBM), and block two-level Erdős-Rényi (BTER) models have been devised to capture those properties. However, the generative algorithms for these models are mostly sequential and take prohibitively long time to generate large-scale graphs. In this paper, we present a novel time and space efficient algorithmic method to generate random graphs using CL, BTER, and SBM models. First, we present an efficient sequential algorithm and an efficient distributed-memory parallel algorithm for the CL model. Our sequential algorithm takes O(m) time and O(Λ) space, where m and Λ are the number of edges and distinct degrees, and our parallel algorithm takes O (m/p + Λ + P) time w.h.p. and O(Λ) space using P processors. These algorithms are almost time optimal since any sequential and parallel algorithms need at least Ω(m) and Ω(m/p) time, respectively. Our algorithms outperform the best known previous algorithms by a significant margin in terms of both time and space. Experimental results on various large-scale networks show that both of our sequential and parallel algorithms require 400–15000 times less memory than the existing sequential and parallel algorithms, respectively, making our algorithms suitable for generating very large-scale networks. Moreover, both of our algorithms are about 3–4 times faster than the existing sequential and parallel algorithms. Finally, we show how our algorithmic method also leads to efficient parallel and sequential algorithms for the SBM and BTER models.

Given a network with groups, such as a contact-network grouped by ages, which are the best groups to immunize to control the epidemic? Equivalently, how to choose best communities in social media like Facebook to stop rumors from spreading? Immunization is an important problem in multiple different domains like epidemiology, public health, cyber security, and social media. Additionally, clearly immunization at group scale (like schools and communities) is more realistic due to constraints in implementations and compliance (e.g., it is hard to ensure specific individuals take the adequate vaccine). Hence, efficient algorithms for such a “group-based” problem can help public-health experts take more practical decisions. However, most prior work has looked into individual-scale immunization. In this paper, we study the problem of controlling propagation at group scale. We formulate a set of novel Group Immunization problems for multiple natural settings (for both threshold and cascade-based contagion models under both node-level and edge-level interventions) and develop multiple efficient algorithms, including provably approximate solutions. Finally, we show the effectiveness of our methods via extensive experiments on real and synthetic datasets.

Detecting and forecasting civil unrest events (protests, strikes, etc.) is of key interest to social scientists and policy makers because these events can lead to significant societal and cultural changes. We analyze protest dynamics in six countries of Latin America on a daily level, from November 2012 through August 2014, using multiple data sources that capture social, political and economic contexts within which civil unrest occurs. We use logistic regression models with Lasso to select a sparse feature set from our diverse datasets, in order to predict the probability of occurrence of civil unrest events in these countries. The models contain predictors extracted from social media sites (Twitter and blogs) and news sources, in addition to volume of requests to Tor, a widely-used anonymity network. Two political event databases and country-specific exchange rates are also used. Our forecasting models are evaluated using a Gold Standard Report (GSR), which is compiled by an independent group of social scientists and experts on Latin America. The experimental results, measured by F1-scores, are in the range 0.68 to 0.95, and demonstrate the efficacy of using a multi-source approach for predicting civil unrest. Case studies illustrate the insights into unrest events that are obtained with our methods.

Given a network with groups, such as a contact-network grouped by ages, which are the best groups to immunize to control the epidemic? Equivalently, how to best choose communities in social networks like Facebook to stop rumors from spreading? Immunization is an important problem in multiple different domains like epidemiology, public health, cyber security and social media. Additionally, clearly immunization at group scale (like schools and communities) is more realistic due to constraints in implementations and compliance (e.g., it is hard to ensure specific individuals take the adequate vaccine). Hence efficient algorithms for such a "group-based" problem can help public-health experts take more practical decisions. However most prior work has looked into individual-scale immunization. In this paper, we study the problem of controlling propagation at group scale. We formulate novel so-called Group Immunization problems for multiple natural settings (for both threshold and cascade-based contagion models under both node-level and edge-level interventions) and develop multiple efficient algorithms, including provably approximate solutions. Finally, we show the effectiveness of our methods via extensive experiments on real and synthetic datasets.

The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the ‘flu-like’ SIS model), it has been shown that an epidemic dies out quickly if the spectral radius of the graph is below a certain threshold that depends on the model parameters. This motivates a strategy to control epidemic spread by reducing the spectral radius of the underlying network. In this paper, we develop a suite of provable approximation algorithms for reducing the spectral radius by removing the minimum cost set of edges (modeling quarantining) or nodes (modeling vaccinations), with different time and quality tradeoffs. Our main algorithm, GREEDYWALK, is based on the idea of hitting closed walks of a given length, and gives an O(log2 n)-approximation, where n denotes the number of nodes; it also performs much better in practice compared to all prior heuristics proposed for this problem. We further present a novel sparsification method to improve its running time. In addition, we give a new primal-dual based algorithm with an even better approximation guarantee (O(log n)), albeit with slower running time. We also give lower bounds on the worst-case performance of some of the popular heuristics. Finally we demonstrate the applicability of our algorithms and the properties of our solutions via extensive experiments on multiple synthetic and real networks.

The spread of epidemics and malware is commonly modeled by diffusion processes on networks. Protective interventions such as vaccinations or installing anti-virus software are used to contain their spread. Typically, each node in the network has to decide its own strategy of securing itself, and its benefit depends on which other nodes are secure, making this a natural game-theoretic setting. There has been a lot of work on network security game models, but most of the focus has been either on simplified epidemic models or homogeneous network structure. We develop a new formulation for an epidemic containment game, which relies on the characterization of the SIS model in terms of the spectral radius of the network. We show in this model that pure Nash equilibria (NE) always exist, and can be found by a best response strategy. We analyze the complexity of finding NE, and derive rigorous bounds on their costs and the Price of Anarchy or PoA (the ratio of the cost of the worst NE to the optimum social cost) in general graphs as well as in random graph models. In particular, for arbitrary power-law graphs with exponent $\beta>2$, we show that the PoA is bounded by $O(T^{2(\beta-1)})$, where $T=\gamma/\alpha$ is the ratio of the recovery rate to the transmission rate in the SIS model. We prove that this bound is tight up to a constant factor for the Chung-Lu random power-law graph model. We study the characteristics of Nash equilibria empirically in different real communication and infrastructure networks, and find that our analytical results can help explain some of the empirical observations.

Analysis of structural properties and dynamics of networks is currently a central topic in many disciplines including Social Sciences, Biology and Business. CINET, a cyber infrastructure for such studies, introduced the concept of supporting network analysis as a service. The basic idea is to allow experts in various disciplines to focus on obtaining domain-specific insights from the results of network analyses instead of worrying about programming details and allocation of computational resources needed to carry out the analyses. A basic version of CINET was released in May 2012. This paper discusses CINET 2.0, a significantly enhanced version that supports complex network analyses through a web portal. CINET 2.0 has already been used for teaching courses related to Network Science at several US universities. In this paper, we discuss how CINET 2.0 significantly extends CINET 1.0 through enhancements to some components and the addition of new components.

As recent pandemics such as SARS and the Swine Flu outbreak have shown, diseases spread very fast in today's interconnected world, making public health an important research area. Some of the basic questions are: How can an outbreak be contained before it becomes an epidemic, and what disease surveillance strategies should be implemented? These problems have been studied traditionally using differential equation methods, which are amenable to analysis and closed form solutions. However, these models are based on complete mixing assumptions, which do not hold for realistic populations, thereby limiting their utility.

We describe the design, implementation, and evaluation of EMBERS, an automated, 24x7 continuous system for forecasting civil unrest across 10 countries of Latin America using open source indicators such as tweets, news sources, blogs, economic indicators, and other data sources. Unlike retrospective studies, EMBERS has been making forecasts into the future since Nov 2012 which have been (and continue to be) evaluated by an independent T&E team (MITRE). Of note, EMBERS has successfully forecast the June 2013 protests in Brazil and Feb 2014 violent protests in Venezuela. We outline the system architecture of EMBERS, individual models that leverage specific data sources, and a fusion and suppression engine that supports trading off specific evaluation criteria. EMBERS also provides an audit trail interface that enables the investigation of why specific predictions were made along with the data utilized for forecasting. Through numerous evaluations, we demonstrate the superiority of EMBERS over baserate methods and its capability to forecast significant societal happenings.

Simple diffusion processes on networks have been used to model, analyze and predict diverse phenomena such as spread of diseases, information and memes. More often than not, the underlying network data is noisy and sampled. This prompts the following natural question: how sensitive are the diffusion dynamics and subsequent conclusions to uncertainty in the network structure? In this paper, we consider two popular diffusion models: Independent cascade (IC) model and Linear threshold (LT) model. We study how the expected number of vertices that are influenced/infected, for particular initial conditions, are affected by network perturbations. Through rigorous analysis under the assumption of a reasonable perturbation model we establish the following main results. (1) For the IC model, we characterize the sensitivity to network perturbation in terms of the critical probability for phase transition of the network. We find that the expected number of infections is quite stable, unless the transmission probability is close to the critical probability. (2) We show that the standard LT model with uniform edge weights is relatively stable under network perturbations. (3) We study these sensitivity questions using extensive simulations on diverse real world networks and find that our theoretical predictions for both models match the observations quite closely. (4) Experimentally, the transient behavior, i.e., the time series of the number of infections, in both models appears to be more sensitive to network perturbations.

Simple diffusion processes on networks have been used to model, analyze and predict diverse phenomena such as spread of diseases, information and memes. More often than not, the underlying network data is noisy and sampled. This prompts the following natural question: how sensitive are the diffusion dynamics and subsequent conclusions to uncertainty in the network structure? In this paper, we consider two popular diffusion models: Independent cascades (IC) model and Linear threshold (LT) model. We study how the expected number of vertices that are influenced/infected, given some initial conditions, are affected by network perturbation. By rigorous analysis under the assumption of a reasonable perturbation model we establish the following main results. (1) For the IC model, we characterize the susceptibility to network perturbation in terms of the critical probability for phase transition of the network. We find the expected number of infections is quite stable, unless the the transmission probability is close to the critical probability. (2) We show that the standard LT model with uniform edge weights is relatively stable under network perturbations. (3) Empirically, the transient behavior, i.e., the time series of the number of infections, in both models appears to be more sensitive to network perturbations. We also study these questions using extensive simulations on diverse real world networks, and find that our theoretical predictions for both models match the empirical observations quite closely.

A fundamental problem in many applications involving social and biological networks is to identify and count the number of embeddings of a given small sub graph in a large graph. Often, they involve dynamic graphs, in which the graph changes incrementally (e.g., by edge addition/deletion). We study the Dynamic Sub graph Enumeration (DSE) Problem, where the goal is to maintain a dynamic data structure to solve the sub graph enumeration problem efficiently when the graph changes incrementally. We develop a new data structure that combines two techniques: (i) the color-coding technique of Alon et al., 2008, for enumerating trees, and (ii) a dynamic data structure for maintaining the h-index of the graph (developed by Eppstein and Spiro, 2009). We derive worst case bounds for the update time in terms of the h-index of the graph and the maximum degree. We also study the empirical performance of our algorithm in a large set of real networks, and find significant improvement over the static methods.

In this paper, we develop the first rigorous distributed algorithm for link scheduling in the SINR model under any length-monotone sub-linear power assignments. Our algorithms give constant factor approximation guarantees, matching the bounds of the sequential algorithms for these problems, with provable bounds on the running time in terms of the graph topology. We also study a related and fundamental problem of local broadcasting for uniform power levels, and obtain similar bounds. These problems are much more challenging in the SINR model than in the more standard graph based interference models, because of the non-locality of the SINR model. Our algorithms are randomized and crucially rely on physical carrier sensing for the distributed communication steps. We find that the specific wireless device capability of duplex/halfduplex communication significantly impacts the performance. Our main technique involves the distributed computation of affectance and a construct called a ruling, which are likely to be useful in other scheduling problems in the SINR model. We also study the empirical performance of our algorithms, and find that the performance depends on the topology, and the approximation ratio is very close to the best sequential algorithm.

We describe a first principles based integrated modeling environment to study urban socio-communication networks which represent not just the physical cellular communication network, but also urban populations carrying digital devices interacting with the cellular network. The modeling environment is designed specifically to understand spectrum demand and dynamic cellular network traffic. One of its key features is its ability to support individual-based models at highly resolved spatial and temporal scales. We have instantiated the modeling environment by developing detailed models of population mobility, device ownership, calling patterns and call network. By composing these models using an appropriate in-built workflow, we obtain an integrated model that represents a dynamic socio-communication network for an entire urban region. In contrast with earlier papers that typically use proprietary data, these models use open source and commercial data sets. The dynamic model represents for a normative day, every individual in an entire region, with detailed demographics, a minute-by-minute schedule of each person's activities, the locations where these activities take place, and calling behavior of every individual. As an illustration of the applicability of the modeling environment, we have developed such a dynamic model for Portland, Oregon comprising of approximately 1.6 million individuals. We highlight the unique features of the models and the modeling environment by describing three realistic case studies.

We study the problem of throughput maximization in multihop wireless networks with end-to-end delay constraints for each session. This problem has received much attention starting with the work of Grossglauser and Tse (2002), and it has been shown that there is a significant tradeoff between the end-to-end delays and the total achievable rate. We develop algorithms to compute such tradeoffs with provable performance guarantees for arbitrary instances, with general interference models. Given a target delay-bound Δ(c) for each session c, our algorithm gives a stable flow vector with a total throughput within a factor of O(log Δm/loglog Δm) of the maximum, so that the per-session (end-to-end) delay is O(((log Δm/loglog Δm)Δ(c))2), where Δm=maxc{Δ(c)}; note that these bounds depend only on the delays, and not on the network size, and this is the first such result, to our knowledge.

Networks are an effective abstraction for representing real systems. Consequently, network science is increasingly used in academia and industry to solve problems in many fields. Computations that determine structure properties and dynamical behaviors of networks are useful because they give insights into the characteristics of real systems. We introduce a newly built and deployed cyberinfrastructure for network science (CINET) that performs such computations, with the following features: (i) it offers realistic networks from the literature and various random and deterministic network generators; (ii) it provides many algorithmic modules and measures to study and characterize networks; (iii) it is designed for efficient execution of complex algorithms on distributed high performance computers so that they scale to large networks; and (iv) it is hosted with web interfaces so that those without direct access to high performance computing resources and those who are not computing experts can still reap the system benefits. It is a combination of application design and cyberinfrastructure that makes these features possible. To our knowledge, these capabilities collectively make CINET novel. We describe the system and illustrative use cases, with a focus on the CINET user.

Relational sub graph analysis, e.g. finding labeled sub graphs in a network, which are isomorphic to a template, is a key problem in many graph related applications. It is computationally challenging for large networks and complex templates. In this paper, we develop SAHAD, an algorithm for relational sub graph analysis using Hadoop, in which the sub graph is in the form of a tree. SAHAD is able to solve a variety of problems closely related with sub graph isomorphism, including counting labeled/unlabeled sub graphs, finding supervised motifs, and computing graph let frequency distribution. We prove that the worst case work complexity for SAHAD is asymptotically very close to that of the best sequential algorithm. On a mid-size cluster with about 40 compute nodes, SAHAD scales to networks with up to 9 million nodes and a quarter billion edges, and templates with up to 12 nodes. To the best of our knowledge, SAHAD is the first such Hadoop based subgraph/subtree analysis algorithm, and performs significantly better than prior approaches for very large graphs and templates. Another unique aspect is that SAHAD is also amenable to running quite easily on Amazon EC2, without needs for any system level optimization.

Designing efficient scheduling and power control algorithms for distributed wireless communication has been a challenging issue, especially in the physical interference model based on SINR constraints. In this paper, we discuss the first local distributed scheduling and power control algorithm in the SINR model that achieves an O(g(L)) approximation factor of the rate region, where O(g(L)) denotes the link diversity. As an intermediate step, we develop a scheduling algorithm in a k-hop interference model, which is used in the analysis of the more general model. Our algorithms are based on random-access and use local queue size information. Exchanging queue size information is challenging, and the complexity of this step is often ignored in prior local distributed algorithms. A novel aspect of our paper is the use of stale and infrequently updated queue size info, which significantly improves the complexity of our algorithms.

3G networks are currently overloaded, due to the increasing popularity of various applications for smartphones. Offloading mobile data traffic through opportunistic communications is a promising solution to partially solve this problem, because there is almost no monetary cost for it. We propose to exploit opportunistic communications to facilitate information dissemination in the emerging Mobile Social Networks (MoSoNets) and thus reduce the amount of mobile data traffic. As a case study, we investigate the target-set selection problem for information delivery. In particular, we study how to select the target set with only k users, such that we can minimize the mobile data traffic over cellular networks. We propose three algorithms, called Greedy, Heuristic, and Random, for this problem and evaluate their performance through an extensive trace-driven simulation study. Our simulation results verify the efficiency of these algorithms for both synthetic and real-world mobility traces. For example, the Heuristic algorithm can offload mobile data traffic by up to 73.66 percent for a real-world mobility trace. Moreover, to investigate the feasibility of opportunistic communications for mobile phones, we implement a proof-of-concept prototype, called Opp-off, on Nokia N900 smartphones, which utilizes their Bluetooth interface for device/service discovery and content transfer.

We study the problem of throughput maximization in multi-hop wireless networks with end-to-end delay constraints for each session. This problem has received much attention starting with the work of Grossglauser and Tse (2002), and it has been shown that there is a significant tradeoff between the end-to-end delays and the total achievable rate. We develop algorithms to compute such tradeoffs with provable performance guarantees for arbitrary instances, with general interference models. Given a target delay-bound Δ(c) for each session c, our algorithm gives a stable flow vector with a total throughput within a factor of O (equation) of the maximum, so that the per-session (end-to-end) delay is O (equation), where Δm= maxc{Δ(c)}; note that these bounds depend only on the delays, and not on the network size, and this is the first such result, to our knowledge.

Large scale realistic simulations of malware on mobile wireless networks have recently become an increasingly important application of high-performance computing. We propose EpiCure - an individual-based, scalable high performance computing oriented modeling environment to study malware propagation over realistic mobile networks. It is designed specifically to work on commodity cluster architectures. EpiCure runs extremely fast for realistic instances that involve: (i) large time-varying networks consisting of millions of heterogeneous individuals with time varying interaction neighborhoods, (ii) dynamic interactions between disease propagation, device behavior, and the exogenous interventions, and (iii) large number of replicated runs necessary for statistically sound estimates about the stochastic epidemic evolution. We find that EpiCure runs several orders of magnitude faster than another comparable simulation tool while delivering similar results. Beyond simple compute speed, EpiCure has been designed so that analysts can easily represent a range of interventions leading to improved human productivity and ease of use. This is an increasingly important metric in high performance computing. We illustrate EpiCure using three case studies that bring out the novel features of EpiCure.

We investigate the tradeoff between two mutually conflicting performance objectives-throughput and delay-for fast, periodic data collection in tree-based sensor networks arbitrarily deployed in 2-D. Two primary factors that affect the data collection rate (throughput) and timeliness (delay) are: 1) efficiency of the link scheduling protocol, and 2) structure of the routing tree in terms of its node degrees and radius. In this paper, we utilize multiple frequency channels and design an efficient link scheduling protocol that gives a constant factor approximation on the optimal throughput in delivering aggregated data from all the nodes to the sink. To minimize the maximum delay subject to a given throughput bound, we also design an (α, β)-bicriteria approximation algorithm to construct a Bounded-Degree Minimum-Radius Spanning Tree, with the radius of the tree at most β times the minimum possible radius for a given degree bound Δ*, and the degree of any node at most Δ*+ α , where α and β are positive constants. Lastly, we evaluate the efficiency of our algorithms on different types of spanning trees and show that multichannel scheduling, combined with optimal routing topologies, can achieve the best of both worlds in terms of maximizing the aggregated data collection rate and minimizing the maximum packet delay.

Aspnes et al introduced an innovative game for modeling the containment of the spread of viruses and worms (security breaches) in a network. In this model, nodes choose to install anti-virus software or not on an individual basis while the viruses or worms start from a node chosen uniformly at random and spread along paths consisting of insecure nodes. They showed the surprising result that a pure Nash Equilibrium always exists when all nodes have identical installation costs and identical infection costs. In this paper we present a substantial generalization of the model of that allows for arbitrary security and infection costs, and arbitrary distributions for the starting point of the attack. More significantly, our model GNS(d) incorporates a network locality parameter d which represents a hop-limit on the spread of infection as accounted for in the strategic decisions, due to either the intrinsic nature of the infection or the extent of neighborhood information that is available to a node. We determine that the network locality parameter plays a key role in the existence of pure Nash equilibria (NE): local (d = 1) and global games (d = ∞) have pure NE, while for GNS(d) games with 11.5n) of achieved for a special case of our global model. We study the characteristics of NE and the quality of our approximations empirically in two distinct classes of graphs: random geometric graphs and power law graphs. We find that in local and global games on these real-world networks, best response dynamics converge in linear or sub-linear time and have costs comparable to the social optimum. Finally, we study the performance of our approximation algorithms, and find that the approximation guarantees with respect to social cost are much better in practice than our theoretical bounds.

Identifying motifs (or commonly occurring subgraphs/templates) has been found to be useful in a number of applications, such as biological and social networks; they have been used to identify building blocks and functional properties, as well as to characterize the underlying networks. Enumerating subgraphs is a challenging computational problem, and all prior results have considered networks with a few thousand nodes. In this paper, we develop a parallel subgraph enumeration algorithm, ParSE, that scales to networks with millions of nodes. Our algorithm is a randomized approximation scheme, that estimates the subgraph frequency to any desired level of accuracy, and allows enumeration of a class of motifs that extends those considered in prior work. Our approach is based on parallelization of an approach called color coding, combined with a stream based partitioning. We also show that ParSE scales well with the number of processors, over a large range.

Large scale realistic epidemic simulations have recently become an increasingly important application of high-performance computing. We propose a parallel algorithm, EpiFast, based on a novel interpretation of the stochastic disease propagation in a contact network. We implement it using a master-slave computation model which allows scalability on distributed memory systems.

Equipping wireless nodes with multiple radios can significantly increase the capacity of wireless networks, by making these radios simultaneously transmit over multiple non-overlapping channels. However, due to the limited number of radios and available orthogonal channels, designing efficient channel assignment and scheduling algorithms in such networks is a major challenge. In this paper, we present provably-good distributed algorithms for simultaneous channel allocation of individual links and packet-scheduling, in software-defined radio (SDR) wireless networks. Our distributed algorithms are very simple to implement, and do not require any coordination even among neighboring nodes. A novel access hash function or random oracle methodology is one of the key drivers of our results. With this access hash function, each radio can know the transmitters' decisions for links in its interference set for each time slot without introducing any extra communication overhead between them. Further, by utilizing the inductive-scheduling technique, each radio can also backoff appropriately to avoid collisions. Extensive simulations demonstrate that our bounds are valid in practice.

Topology control in ad hoc networks is a multi-criteria optimization problem involving (contradictory) objectives of connectivity, interference, and power minimization. Additionally, nodes can be unreliable, which adds another dimension to an already challenging problem. In this paper, we study topology control problems in ad hoc networks under node failures for arbitrary node distributions. We consider a simple and natural stochastic failure model, in which each node can fail independently with a given probability. The topology control problem under stochastic failures is to choose a power level for each node and a subset of edges such that the residual graph (i.e., the graph formed by the nodes which have not failed) is connected and can be scheduled efficiently, with high probability. We develop provably efficient bi-criteria approximation algorithms for this problem that simultaneously minimize power, reduce interference, and ensure that the surviving graph is connected with high probability. Our algorithms can be implemented efficiently in a distributed manner.

Fast and periodic collection of aggregated data is of considerable interest for mission-critical and continuous monitoring applications in sensor networks. In the many-to-one communication paradigm known as convergecast, we consider scenarios where data packets are aggregated at each hop en route to a sink node along a tree-based routing topology and focus on maximizing the data collection rate at the sink by employing TDMA scheduling and multiple frequency channels. Our key result in the paper lies in proving that minimizing the schedule length for an arbitrary network in the presence of multiple frequencies is NP-hard, and in designing approximation algorithms with worst-case provable performance guarantees for geometric networks. In particular, we design a constant factor approximation for networks modeled as unit disk graphs (UDG) where every node has a uniform transmission range, and a O(Delta(T)log n) approximation for general disk graphs where nodes have different transmission ranges; n is the number of nodes in the network and Delta(T) is the maximum node degree on a given routing tree T. We also prove that a constant factor approximation is achievable on UDG even for unknown routing topologies so long as the maximum node degree in the tree is bounded by a constant. We also show that finding the minimum number of frequencies required to remove all the interfering links in an arbitrary network in NP-hard. We give an upper bound on the maximum number of such frequencies required and propose a polynomial time algorithm that minimizes the schedule length under this scenario. Finally, we evaluate our algorithms through simulations and show various trends in performance for different network parameters.

Peer-to-peer (P2P) technology provides a scalable solution in multimedia streaming. Many streaming applications, such as IPTV and video conferencing, have rigorous constraints on end-to-end delays. Obtaining assurances on meeting those delay constraints in dynamic and heterogenous network environments is a challenge. In this paper, we devise a streaming scheme which minimizes the maximum end-to-end streaming delay for a mesh-based overlay network paradigm. We first formulate the minimum-delay P2P streaming problem, called the MDPS problem, and prove its NP-completeness. We then present a polynomial-time approximation algorithm to this problem, and show that the performance of our algorithm is bounded by a ratio of O. Our simulation study reveals the effectiveness of our algorithm, and shows a reasonable message overhead.

We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming-, quadratic programming-, and convex programming-relaxations for scheduling to minimize completion time, makespan, and other well-studied objective functions. This algorithm leads to the following applications for the general setting of unrelated parallel machines: (i) a bicriteria algorithm for a schedule whose weighted completion-time and makespan simultaneously exhibit the current-best individual approximations for these criteria; (ii) better-than-two approximation guarantees for scheduling to minimize the L p norm of the vector of machine-loads, for all 1 < p < ∞; and (iii) the first constant-factor multicriteria approximation algorithms that can handle the weighted completion-time and any given collection of integer L p norms. Our algorithm has a natural interpretation as a melding of linear-algebraic and probabilistic approaches. Via this view, it yields a common generalization of rounding theorems due to Karp et al. [1987] and Shmoys & Tardos [1993], and leads to improved approximation algorithms for the problem of scheduling with resource-dependent processing times introduced by Grigoriev et al. [2007].

Traditionally, the performance of distributed algorithms has been measured in terms of time and message complexity.Message complexity concerns the number of messages transmitted over all the edges during the course of the algorithm. However, in energy-constrained ad hoc wireless networks (e.g., sensor networks), energy is a critical factor in measuring the efficiency of a distributed algorithm. Transmitting a message between two nodes has an associated cost (energy) and moreover this cost can depend on the two nodes (e.g., the distance between them among other things). Thus in addition to the time and message complexity, it is important to consider energy complexity that accounts for the total energy associated with the messages exchanged among the nodes in a distributed algorithm. This paper addresses the minimum spanning tree (MST) problem, a fundamental problem in distributed computing and communication networks. We study energy-efficient distributed algorithms for the Euclidean MST problem assuming random distribution of nodes. We show a non-trivial lower bound ofΩ(log n)on the energy complexity of any distributed MST algorithm. We then give an energy-optimal distributed algorithm that constructs an optimal MST with energy complexityO(log n)on average andO(log n log log n)with high probability. This is an improvement over the previous best known bound on the average energy complexity ofΩ(log2). Our energy-optimal algorithm exploits a novel property of the giant component of sparse random geometric graphs. All of the above results assume that nodes do not know their geometric coordinates. If the nodes know their own coordinates, then we give an algorithm withO(1)energy complexity (which is the best possible) that gives anO(1)approximation to the MST.

While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time; this makes these algorithms impractical for resource-constrained networks such as ad hoc wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy efficient for being practical. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called Nearest Neighbor Tree (NNT) algorithms for energy-efficient construction of MSTs in a wireless ad hoc setting. We assume that the nodes are uniformly distributed in a unit square and show provable bounds on the performance with respect to both the quality of the spanning tree produced and the energy needed to construct them. In particular, we show that NNT produces a close approximation to the MST, and they can be maintained dynamically with polylogarithmic number of rearrangements under node insertions/deletions. We also perform extensive simulations of our algorithms. We tested our algorithms on both uniformly random distributions of nodes, and on a realistic distributions of nodes in an urban setting. Simulations validate the theoretical results and show that the bounds are much better in practice.

We study the problem of total throughput maximization in arbitrary multi-hop wireless networks, with constraints on the total power usage (denoted by PETM), when nodes have the capability to adaptively choose their power levels, which is the case with software defined radio devices. The underlying interference graph changes when power levels change, making PETM a complex cross-layer optimization problem. We develop a linear programming formulation for this problem, that leads to a constant factor approximation to the total throughput rate, for any given bound on the total power usage. Our result is a rigorously provable worst case approximation guarantee, which holds for any instance. Our formulation is generic and can accommodate different interference models and objective functions. We complement our theoretical analysis with simulations and compute the explicit tradeoffs between fairness, total throughput and power usage.

A fundamental problem in wireless networks is to estimate its throughput capacity - given a set of wireless nodes, and a set of connections, what is the maximum rate at which data can be sent on these connections. Most of the research in this direction has focused on either random distributions of points, or has assumed simple graph-based models for wireless interference. In this paper, we study capacity estimation problem using the more general Signal to Interference Plus Noise Ratio (SINR) model for interference, on arbitrary wireless networks. The problem becomes much harder in this setting, because of the non-locality of the SINR model. Recent work by Moscibroda et al. (2006) has shown that the throughput in this model can differ from graph based models significantly. We develop polynomial time algorithms to provably approximate the total throughput in this setting.

We study the throughput capacity of wireless networks which employ (asynchronous) random-access scheduling as opposed to deterministic scheduling. The central question we answer is: how should we set the channel-access probability for each link in the network so that the network operates close to its optimal throughput capacity? We design simple and distributed channel-access strategies for random-access networks which are provably competitive with respect to the optimal scheduling strategy, which is deterministic, centralized, and computationally infeasible. We show that the competitiveness of our strategies are nearly the best achievable via random-access scheduling, thus establishing fundamental limits on the performance of random- access. A notable outcome of our work is that random access compares well with deterministic scheduling when link transmission durations differ by small factors, and much worse otherwise. The distinguishing aspects of our work include modeling and rigorous analysis of asynchronous communication, asymmetry in link transmission durations, and hidden terminals under arbitrary link-conflict based wireless interference models.

Traditionally, the performance of distributed algorithms has been measured in terms of time and message complexity. Message complexity concerns the number of messages transmitted over all the edges during the course of the algorithm. However, in energy-constraint radio or wireless networks (e.g., sensor networks), energy is a critical factor in measuring the efficiency of a distributed algorithm. Transmitting a message between two nodes has an associated cost (energy) and moreover this cost can depend on the two nodes (e.g., the distance between them among other things). Thus in addition to the time and message complexity, it is important to consider energy complexity that accounts for the total energy associated with the messages exchanged among the nodes in a distributed algorithm, and design energy-efficient distributed algorithms for energy-constraint networks.

Recently, there has been substantial interest in the design of cross-layer protocols for wireless networks. These protocols optimize certain performance metric(s) of interest (e.g. latency, energy, rate) by jointly optimizing the performance of multiple layers of the protocol stack. Algorithm designers often use geometric-graph-theoretic models for radio interference to design such cross-layer protocols. In this paper we study the problem of designing cross-layer protocols for multi-hop wireless networks using a more realistic Signal to Interference plus Noise Ratio (SINR) model for radio interference. The following cross-layer latency minimization problem is studied: Given a set V of transceivers, and a set of source-destination pairs, (i) choose power levels for all the transceivers, (ii) choose routes for all connections, and (iii) construct an end-to-end schedule such that the SINR constraints are satisfied at each time step so as to minimize the make-span of the schedule (the time by which all packets have reached their respective destinations). We present a polynomial-time algorithm with provable worst-case performance guarantee for this cross-layer latency minimization problem. As corollaries of the algorithmic technique we show that a number of variants of the cross-layer latency minimization problem can also be approximated efficiently in polynomial time. Our work extends the results of Kumar et al. (Proc. SODA, 2004) and Moscibroda et al. (Proc. MOBIHOC, 2006). Although our algorithm considers multiple layers of the protocol stack, it can naturally be viewed as compositions of tasks specific to each layer --- this allows us to improve the overall performance while preserving the modularity of the layered structure.

We address the problem of constrained exploration of an unknown graph G = ( V , E ) from a given start node s with either a tethered robot or a robot with a fuel tank of limited capacity, the former being a tighter constraint. In both variations of the problem, the robot can only move along the edges of the graph, for example, it cannot jump between nonadjacent nodes. In the tethered robot case, if the tether (rope) has length l , then the robot must remain within distance l from the start node s . In the second variation, a fuel tank of limited capacity forces the robot to return to s after traversing C edges. The efficiency of algorithms for both variations of the problem is measured by the number of edges traversed during the exploration. We present an algorithm for a tethered robot that explores the graph in Θ(| E |) edge traversals. The problem of exploration using a robot with a limited fuel tank capacity can be solved with a simple reduction from the tethered robot case and also yields a Θ(| E |) algorithm. This improves on the previous best-known bound of O (| E | + | V |log 2 | V |). Since the lower bound for the graph exploration problems is Ω(| E |), our algorithm is optimal within a constant factor.

We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming, quadratic programming, and convex programming-relaxations for scheduling to minimize completion time, makespan, and other well-studied objective functions. We obtain the following applications for the general setting of unrelated parallel machines: (i) a bicriteria algorithm for a schedule whose weighted completion-time and makespan simultaneously exhibit the current-best individual approximations for these criteria (3/2 and 2, respectively); (ii) better-than-two approximation guarantees for scheduling under the L/sub p/ norm for all 1 < p < /spl infin/, improving on the 2-approximation algorithms of Azar & Epstein; and (iii) the first constant-factor multicriteria approximation algorithms that handle the weighted completion-time and any given collection of integer L/sub p/ norms. Our algorithm yields a common generalization of rounding theorems due to Karp et al and Shmoys & Tardos; among other applications, this yields an improved approximation for scheduling with resource-dependent processing times studied by Grigoriev et al.

This paper considers two inter-related questions: (i) Given a wireless ad-hoc network and a collection of source-destination pairs {(si,ti)}, what is the maximum throughput capacity of the network, i.e. the rate at which data from the sources to their corresponding destinations can be transferred in the network? (ii) Can network protocols be designed that jointly route the packets and schedule transmissions at rates close to the maximum throughput capacity? Much of the earlier work focused on random instances and proved analytical lower and upper bounds on the maximum throughput capacity. Here, in contrast, we consider arbitrary wireless networks. Further, we study the algorithmic aspects of the above questions: the goal is to design provably good algorithms for arbitrary instances. We develop analytical performance evaluation models and distributed algorithms for routing and scheduling which incorporate fairness, energy and dilation (path-length) requirements and provide a unified framework for utilizing the network close to its maximum throughput capacity.Motivated by certain popular wireless protocols used in practice, we also explore "shortest-path like" path selection strategies which maximize the network throughput. The theoretical results naturally suggest an interesting class of congestion aware link metrics which can be directly plugged into several existing routing protocols such as AODV, DSR, etc. We complement the theoretical analysis with extensive simulations. The results indicate that routes obtained using our congestion aware link metrics consistently yield higher throughput than hop-count based shortest path metrics.

There has recently been renewed interest among various research communities in understanding the structure of social and infrastructure networks. Motivated by this line of research, we conduct an in-depth structural analysis of large ad hoc networks derived by placing nodes randomly as well as by placing them in realistic urban environments, a scenario that is rapidly gaining interest (K. Jain, et al, 2003). We use structural analysis in two illustrative settings. First, we use it to study the performance of network protocols. Our results indicate that structural analysis of interference graphs that model ad hoc networks can yield a good first order prediction of the overall protocol performance. Second, we study the robustness of a network to random node and edge failures. This study is important in the context of ad hoc networks wherein one expects nodes/edges to fail due various natural or system dependent reasons. The experimental results presented in this paper show the following: (i) structural properties of ad hoc networks depend crucially on the spatial distribution of the nodes. (ii) Structural properties of the network significantly affect the performance of protocols. (iii) Graph theoretic measures can provide good first order insights into the network protocol performance. (iv) The measures are also useful in characterizing the robustness of such networks.

We consider the problem of determining the maximum capacity of the media access (MAC) layer in wireless ad hoc networks. Due to spatial contention for the shared wireless medium, not all nodes can concurrently transmit packets to each other in these networks. The maximum number of possible concurrent transmissions is, therefore, an estimate of the maximum network capacity, and depends on the MAC protocol being used. We show that for a large class of MAC protocols based on virtual carrier sensing using RTS/CTS messages, which includes the popular IEEE 802.11 standard, this problem may be modeled as a maximum Distance-2 matching ( D2EMIS) in the underlying wireless network: Given a graph G(V,E), find a set of edges E'/spl sube/E such that no two edges in E' are connected by another edge in E. D2EMIS is NP-complete. Our primary goal is to show that it can be approximated efficiently in networks that arise in practice. We do this by focusing on an admittedly simplistic, yet natural, graph-theoretic model for ad hoc wireless networks based on disk graphs, where a node can reach all other nodes within some distance (nodes may have unequal reach distances). We show that our approximation yields good capacity bounds. Our work is the first attempt at characterizing an important "maximum" measure of wireless network capacity, and can be used to shed light on previous topology formation protocols like Span and GAF that attempt to produce "good" or "capacity-preserving" topologies, while allowing nodes to alternate between sleep and awake states. Our work shows an efficient way to compute an upper bound on maximum wireless network capacity, thereby allowing topology formation algorithms to determine how close they are to optimal. We also outline a distributed algorithm for the problem for unit disk graphs, and briefly discuss extensions of our results to: 1) different node interference models; 2) directional antennas; and 3) other transceiver connectivity structures besides disk graphs.

We give an $O(\sqrt{\log n})$ factor approximation algorithm for covering a rectilinear polygon with holes using axis-parallel rectangles. This is the first polynomial time approximation algorithm for this problem with an $o(\log n)$ approximation factor.

We show that no Markovian coupling argument can prove rapid mixing of the Jerrum-Sinclair Markov chain for sampling almost uniformly from the set of perfect and near perfect matchings of a given graph. In particular, we show that there exists a bipartite graph G such that any Markovian coupling argument on the Jerrum-Sinclair Markov chain for G must necessarily take time exponential in the number of vertices in G. This holds even when the coupling argument is time-variant, i.e., the transition probabilities used by the coupling process depend upon the history of the process. In contrast, the above Markov chain on G has been shown to mix in polynomial time using conductance arguments.