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.

Large-scale livestock operations pose significant risks to human health and the environment, while also being vulnerable to threats such as infectious diseases and extreme weather events. As the number of such operations continues to grow, accurate and scalable mapping has become increasingly important. In this work, we present an infrastructure-first, explainable pipeline for identifying and characterizing Concentrated Animal Feeding Operations (CAFOs) from aerial and satellite imagery. Our method (i) detects candidate infrastructure (e.g., barns, feedlots, manure lagoons, silos) with a domain-tuned YOLOv8 detector, then derives SAM2 masks from these boxes and filters component-specific criteria; (ii) extracts structured descriptors (e.g., counts, areas, orientations, and spatial relations) and fuses them with deep visual features using a lightweight spatial cross-attention classifier; and (iii) outputs both CAFO type predictions and mask-level attributions that link decisions to visible infrastructure. Through comprehensive evaluation, we show that our approach achieves state-of-the-art performance, with Swin-B+PRISM-CAFO surpassing the best performing baseline by up to 15%. Beyond strong predictive performance across diverse U.S. regions, we run systematic gradient–activation analyses that quantify the impact of domain priors and show how specific infrastructure (e.g., barns, lagoons) shapes classification decisions. We release code, infrastructure masks, and descriptors to support transparent, scalable monitoring of livestock infrastructure, enabling risk modeling, change detection, and targeted regulatory action. Github: https://github.com/Nibir088/PRISM-CAFO.

Considering the difficulty of interpreting generative model output, there is significant current research focused on determining meaningful evaluation metrics. Several recent approaches utilize "precision" and "recall," borrowed from the classification domain, to individually quantify the output fidelity (realism) and output diversity (representation of the real data variation), respectively. With the increase in metric proposals, there is a need for a unifying perspective, allowing for easier comparison and clearer explanation of their benefits and drawbacks. To this end, we unify a class of kth-nearest neighbors (kNN)-based metrics under an information-theoretic lens using approaches from kNN density estimation. Additionally, we propose a tri-dimensional metric composed of Precision Cross-Entropy (PCE), Recall Cross-Entropy (RCE), and Recall Entropy (RE), which separately measure fidelity and two distinct aspects of diversity, inter- and intra-class. Our domain-agnostic metric, derived from the information-theoretic concepts of entropy and cross-entropy, can be dissected for both sample- and mode-level analysis. Our detailed experimental results demonstrate the sensitivity of our metric components to their respective qualities and reveal undesirable behaviors of other metrics.

We consider a setting where goods are allocated to agents by way of an allocation platform (e.g., a matching platform). An “allocation facilitator” aims to increase the overall utility/social-good of the allocation by encouraging (some of the) agents to relax (some of) their restrictions. At the same time, the advice must not hurt agents who would otherwise be better off. Additionally, the facilitator may be constrained by a “bound” (a.k.a. ‘budget’), limiting the number and/or type of restrictions it may seek to relax. We consider the facilitator’s optimization problem of choosing an optimal set of restrictions to request to relax under the aforementioned constraints. Our contributions are three-fold: (i) We provide a formal definition of the problem, including the participation guarantees to which the facilitator should adhere. We define a hierarchy of participation guarantees and also consider several social-good functions. (ii) We provide polynomial algorithms for solving various versions of the associated optimization problems, including one-to-one and many-to-one allocation settings. (iii) We demonstrate the benefits of such facilitation and relaxation, and the implications of the different participation guarantees, using extensive experimentation on three real-world datasets.

Accurate canal network mapping is essential for water management, including irrigation planning and infrastructure maintenance. State-of-the-art semantic segmentation models for infrastructure mapping, such as roads, rely on large, well-annotated remote sensing datasets. However, incomplete or inadequate ground truth can hinder these learning approaches. Many infrastructure networks have graph-level properties such as reachability to a source (like canals) or connectivity (roads) that can be leveraged to improve these existing ground truth. This paper develops a novel iterative framework IGraSS, combining a semantic segmentation module—incorporating RGB and additional modalities (NDWI, DEM)—with a graph-based ground-truth refinement module. The segmentation module processes satellite imagery patches, while the refinement module operates on the entire data viewing the infrastructure network as a graph. Experiments show that IGraSS reduces unreachable canal segments from ~18% to ~3%, and training with refined ground truth significantly improves canal identification. IGraSS serves as a robust framework for both refining noisy ground truth and mapping canal networks from remote sensing imagery. We also demonstrate the effectiveness and generalizability of IGraSS using road networks as an example, applying a different graph-theoretic constraint to complete road networks.

Accurate mapping of irrigation methods is crucial for sustainable agricultural practices and food systems. However, existing models that rely solely on spectral features from satellite imagery are ineffective due to the complexity of agricultural landscapes and limited training data, making this a challenging problem. We present Knowledge-Informed Irrigation Mapping (KIIM), a novel Swin-Transformer based approach that uses (i) a specialized projection matrix to encode crop to irrigation probability, (ii) a spatial attention map to identify agricultural lands from non-agricultural lands, (iii) bi-directional cross-attention to focus complementary information from different modalities, and (iv) a weighted ensemble for combining predictions from images and crop information. Our experimentation on five states in the US shows up to 22.9% (IoU) improvement over baseline with a 71.4% (IoU) improvement for hard-to-classify drip irrigation. In addition, we propose a two-phase transfer learning approach to enhance cross-state irrigation mapping, achieving a 51% IoU boost in a state with limited labeled data. The ability to achieve baseline performance with only 40% of the training data highlights its efficiency, reducing the dependency on extensive manual labeling efforts and making large-scale, automated irrigation mapping more feasible and cost-effective. Code: https://github.com/Nibir088/KIIM

We introduce IrrMap, the first large-scale dataset (1.1 million patches) for irrigation method mapping across regions. IrrMap consists of multi-resolution satellite imagery from LandSat and Sentinel, along with key auxiliary data such as crop type, land use, and vegetation indices. The dataset spans 1,668,899 farms and 11,443,492 acres across multiple western U.S. states from 2013 to 2023, providing a rich and diverse foundation for irrigation analysis and ensuring geospatial alignment and quality control. The dataset is ML-ready, with standardized 224×224 GeoTIFF patches, the multiple input modalities, carefully chosen train-test-split data, and accompanying dataloaders for seamless deep learning model training and benchmarking in irrigation mapping. The dataset is also accompanied by a complete pipeline for dataset generation, enabling researchers to extend IrrMap to new regions for irrigation data collection or adapt it with minimal effort for other similar applications in agricultural and geospatial analysis. We also analyze the irrigation method distribution across crop groups, spatial irrigation patterns (using Shannon diversity indices), and irrigated area variations for both LandSat and Sentinel, providing insights into regional and resolution-based differences. To promote further exploration, we openly release IrrMap, along with the derived datasets, benchmark models, and pipeline code, through a GitHub repository: https://github.com/Nibir088/IrrMap and Data repository: https://huggingface.co/Nibir/IrrMap, providing comprehensive documentation and implementation details.

The lack of fine-grained, large-scale datasets on water availability presents a critical barrier to applying machine learning (ML) for agricultural water management. Since there are multiple natural and anthropogenic factors that influence water availability, incorporating diverse multimodal features can significantly improve modeling performance. However, integrating such heterogeneous data is challenging due to spatial misalignments, inconsistent formats, semantic label ambiguities, and class imbalances. To address these challenges, we introduce IRRISIGHT, a large-scale, multimodal dataset spanning 20 U.S. states. It consists of 1.4 million pixel-aligned 224×224 patches that fuse satellite imagery with rich environmental attributes. We develop a robust geospatial fusion pipeline that aligns raster, vector, and point-based data on a unified 10m grid, and employ domain-informed structured prompts to convert tabular attributes into natural language. With irrigation type classification as a representative problem, the dataset is AI-ready, offering a spatially disjoint train/test split and extensive benchmarking with both vision and vision–language models. Our results demonstrate that multimodal representations substantially improve model performance, establishing a foundation for future research on water availability.https://github.com/Nibir088/IRRISIGHThttps://huggingface.co/datasets/OBH30/IRRISIGHT

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.

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.

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.

Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which they want to be matched. Viewing such an application as a multi-round matching problem on a bipartite compatibility graph between agents and resources, we show that a solution (i.e., a set of matchings, with one matching per round) can be found efficiently if one exists. To cope with situations where a solution does not exist, we consider two extensions. In the first extension, a benefit function is defined for each agent and the objective is to find a multi-round matching to maximize the total benefit. For a general class of benefit functions satisfying certain properties (including diminishing returns), we show that this multi-round matching problem is efficiently solvable. This class includes utilitarian and Rawlsian welfare functions. For another benefit function, we show that the maximization problem is NP-hard. In the second extension, the objective is to generate advice to each agent (i.e., a subset of requirements to be relaxed) subject to a budget constraint so that the agent can be matched. We show that this budget-constrained advice generation problem is NP-hard. For this problem, we develop an integer linear programming formulation as well as a heuristic based on local search. We experimentally evaluate our algorithms on synthetic networks and apply them to two real-world situations: shared office spaces and matching courses to classrooms.

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.

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.

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.

Developing techniques to infer the behavior of networked social systems has attracted a lot of attention in the literature. Using a discrete dynamical system to model a networked social system, the problem of inferring the behavior of the system can be formulated as the problem of learning the local functions of the dynamical system. We investigate the problem assuming an active form of interaction with the system through queries. We consider two classes of local functions (namely, symmetric and threshold functions) and two interaction modes, namely batch (where all the queries must be submitted together) and adaptive (where the set of queries submitted at a stage may rely on the answers to previous queries). We establish bounds on the number of queries under both batch and adaptive query modes using vertex coloring and probabilistic methods. Our results show that a small number of appropriately chosen queries are provably sufficient to correctly learn all the local functions. We develop complexity results which suggest that, in general, the problem of generating query sets of minimum size is computationally intractable. We present efficient heuristics that produce query sets under both batch and adaptive query modes. Also, we present a query compaction algorithm that identifies and removes redundant queries from a given query set. Our algorithms were evaluated through experiments on over 20 well-known networks.

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.

In Boolean games, each agent controls a set of Boolean variables and has a goal represented by a propositional formula. We study inference problems in Boolean games assuming the presence of a PRINCIPAL who has the ability to control the agents and impose taxation schemes. Previous work used taxation schemes to guide a game towards certain equilibria. We present algorithms that show how taxation schemes can also be used to infer agents' goals. We present experimental results to demonstrate the efficacy our algorithms. We also consider goal inference when only limited information is available in response to a query.

In anagram games, players are provided with letters for forming as many words as possible over a specified time duration. Anagram games have been used in controlled experiments to study problems such as collective identity, effects of goal-setting, internal-external attributions, test anxiety, and others. The majority of work on anagram games involves individual players. Recently, work has expanded to group anagram games where players cooperate by sharing letters. In this work, we analyze experimental data from online social networked experiments of group anagram games. We develop mechanistic and data-driven models of human decision-making to predict detailed game player actions (e.g., what word to form next). With these results, we develop a composite agent-based modeling and simulation platform that incorporates the models from data analysis. We compare model predictions against experimental data, which enables us to provide explanations of human decision-making and behavior. Finally, we provide illustrative case studies using agent-based simulations to demonstrate the efficacy of models to provide insights that are beyond those from experiments alone.

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.

Abduction is an inference approach that uses data and observations to identify plausible (and preferably, best) explanations for phenomena. Applications of abduction (e.g., robotics, genetics, image understanding) have largely been devoid of human behavior. Here, we devise and execute an iterative abductive analysis process that is driven by the social sciences: behaviors and interactions among groups of human subjects. One goal is to understand intra-group cooperation and its effect on fostering collective identity. We build an online game platform; perform and analyze controlled laboratory experiments; form hypotheses; build, exercise, and evaluate network-based agent-based models; and evaluate the hypotheses in multiple abductive iterations, improving our understanding as the process unfolds. While the experimental results are of interest, the paper's thrust is methodological, and indeed establishes the potential of iterative abductive looping for the (computational) social sciences.

The problem of inferring unknown parameters of a networked social system is of considerable practical importance. We consider this problem for the independent cascade model using an active query framework. More specifically, given a network whose edge probabilities are unknown, the goal is to infer the probability value on each edge by querying the system. The optimization objective is to use as few queries as possible in carrying out the inference. We present approximation algorithms that provide provably good estimates of edge probabilities. We also present results from an experimental evaluation of our algorithms on several real-world networks.

We develop a general data-driven methodology that yields network representations of agricultural flows pertaining to the spread of invasive species. The methodology synthesizes sparse, diverse, noisy and incomplete data that is typically available to build realistic spatiotemporal network representations. We illustrate the methodology by modeling the seasonal flow of the tomato crop in Nepal between major domestic markets. Through dynamical analysis of the network, we study its role in the spread of a major pest of tomato, Tuta absoluta, an emerging outbreak in this country. In the absence of high-resolution pest distribution data, we apply a novel ranking-based inference approach to establish that tomato trade is a driving factor in the rapid spread of this pest.

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.

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.

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.

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.

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.

We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if their corresponding vertices are adjacent. In fact, we construct a representation in which any two intersecting boxes touch just at their boundaries.

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.

We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if their corresponding vertices are adjacent. In fact, we construct a representation in which any two intersecting boxes just touch at their boundaries. Further, this construction can be realized in linear time.

A k-box B=(R_1,R_2,...,R_k), where each R_i is a closed interval on the real line, is defined to be the Cartesian product R_1 X R_2 X ... X R_k. If each R_i is a unit length interval, we call B a k-cube. Boxicity of a graph G, denoted as box(G), is the minimum integer k such that G is an intersection graph of k-boxes. Similarly, the cubicity of G, denoted as cub(G), is the minimum integer k such that G is an intersection graph of k-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan. Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/0607092, 2006.] that, for a graph G with maximum degree \Delta, cub(G) <= \lceil 4(\Delta +1) ln n\rceil. In this paper we show that, for a k-degenerate graph G, cub(G) <= (k+2) \lceil 2e log n \rceil. Since k is at most \Delta and can be much lower, this clearly is a stronger result. We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 log n\rceil + 1) dimensional cube representation for G. The crossing number of a graph G, denoted as CR(G), is the minimum number of crossing pairs of edges, over all drawings of G in the plane. An important consequence of the above result is that if the crossing number of a graph G is t, then box(G) is O(t^{1/4}{\lceil log t\rceil}^{3/4}) . This bound is tight upto a factor of O((log t)^{3/4}). Let (P,\leq) be a partially ordered set and let G_{P} denote its underlying comparability graph. Let dim(P) denote the poset dimension of P. Another interesting consequence of our result is to show that dim(P) \leq 2(k+2) \lceil 2e \log n \rceil, where k denotes the degeneracy of G_{P}. Also, we get a deterministic algorithm that runs in O(n^2k) time to construct a 16k(\lceil 2.42 log n\rceil + 1) sized realizer for P. As far as we know, though very good upper bounds exist for poset dimension in terms of maximum degree of its underlying comparability graph, no upper bounds in terms of the degeneracy of the underlying comparability graph is seen in the literature.

Let G be a simple, undirected, finite graph with vertex set $V(G)$ and edge set $E(G)$. A k-dimensional box is a Cartesian product of closed intervals $[a_1,b_1]\times [a_2,b_2]\times\cdots\times [a_k,b_k]$. The boxicity of G, box$(G)$, is the minimum integer k such that G can be represented as the intersection graph of k-dimensional boxes; i.e., each vertex is mapped to a k-dimensional box and two vertices are adjacent in G if and only if their corresponding boxes intersect. Let $\mathcal{P}=(S,P)$ be a poset, where S is the ground set and P is a reflexive, antisymmetric and transitive binary relation on S. The dimension of $\mathcal{P}$, $\dim(\mathcal{P})$, is the minimum integer t such that P can be expressed as the intersection of t total orders. Let $G_{\mathcal{P}}$ be the underlying comparability graph of $\mathcal{P}$; i.e., S is the vertex set and two vertices are adjacent if and only if they are comparable in $\mathcal{P}$. It is a well-known fact that posets with the same underlying comparability graph have the same dimension. The first result of this paper links the dimension of a poset to the boxicity of its underlying comparability graph. In particular, we show that for any poset $\mathcal{P}$, box$(G_{\mathcal{P}})/(\chi(G_{\mathcal{P}})-1) \le \dim(\mathcal{P})\le 2\mbox{box}(G_{\mathcal{P}})$, where $\chi(G_{\mathcal{P}})$ is the chromatic number of $G_{\mathcal{P}}$ and $\chi(G_{\mathcal{P}})\ne1$. It immediately follows that if $\mathcal{P}$ is a height-2 poset, then box$(G_{\mathcal{P}})\le \dim(\mathcal{P})\le 2\mbox{box}(G_{\mathcal{P}})$ since the underlying comparability graph of a height-2 poset is a bipartite graph. The second result of the paper relates the boxicity of a graph G with a natural partial order associated with the extended double cover of G, denoted as $G_c$: Note that $G_c$ is a bipartite graph with partite sets A and B which are copies of $V(G)$ such that, corresponding to every $u\in V(G)$, there are two vertices $u_A\in A$ and $u_B\in B$ and $\{u_A,v_B\}$ is an edge in $G_c$ if and only if either $u=v$ or u is adjacent to v in G. Let $\mathcal{P}_c$ be the natural height-2 poset associated with $G_c$ by making A the set of minimal elements and B the set of maximal elements. We show that $\frac{\mbox{box}(G)}{2} \le \dim(\mathcal{P}_c) \le 2\mbox{box}(G)+4$. These results have some immediate and significant consequences. The upper bound $\dim(\mathcal{P})\le 2\mbox{box}(G_\mathcal{P})$ allows us to derive hitherto unknown upper bounds for poset dimension such as $\dim(\mathcal{P})\le 2\mbox{ tree width }(G_{\mathcal{P}})+4$, since boxicity of any graph is known to be at most its tree width $+\; 2$. In the other direction, using the already known bounds for partial order dimension we get the following: (1) The boxicity of any graph with maximum degree $\Delta$ is $O(\Delta\log^2\Delta)$, which is an improvement over the best-known upper bound of $\Delta^2+2$. (2) There exist graphs with boxicity $\Omega(\Delta\log\Delta)$. This disproves a conjecture that the boxicity of a graph is $O(\Delta)$. (3) There exists no polynomial-time algorithm to approximate the boxicity of a bipartite graph on n vertices with a factor of $O(n^{0.5-\epsilon})$ for any $\epsilon>0$ unless $NP=ZPP$.

We propose a framework for orthonormal symmetric wavelet transform given a cyclic zero-phase half band filter. The scheme consists of a design for cyclic wavelet transform with real symmetric filters based on the perfect reconstruction circular convolution filter banks accompanied by an implementation in the discrete trigonometric transform domain. This is followed by a brief discussion on its performance in the context of applications such as image compression and implementation of symmetric wavelet transforms based on bandlimited wavelets.