Graph condensation has emerged as a promising avenue to enable scalable training of GNNs by compressing the training dataset while preserving essential graph characteristics. Our study uncovers significant shortcomings in current graph condensation techniques. First, the majority of the algorithms paradoxically require training on the full dataset to perform condensation. Second, due to their gradient-emulating approach, these methods require fresh condensation for any change in hyperparameters or GNN architecture, limiting their flexibility and reusability. To address these challenges, we present Bonsai, a novel graph condensation method empowered by the observation that *computation trees* form the fundamental processing units of message-passing GNNs. Bonsai condenses datasets by encoding a careful selection of *exemplar* trees that maximize the representation of all computation trees in the training set. This unique approach imparts Bonsai as the first linear-time, model-agnostic graph condensation algorithm for node classification that outperforms existing baselines across $7$ real-world datasets on accuracy, while being $22$ times faster on average. Bonsai is grounded in rigorous mathematical guarantees on the adopted approximation strategies, making it robust to GNN architectures, datasets, and parameters.

Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved improved approximation quality compared to non-neural approaches, they face significant challenges: (1) They require large amounts of ground truth data, which is itself NP-hard to compute. (2) They operate as black boxes, offering limited interpretability. (3) They lack cross-domain generalization, necessitating expensive retraining for each new dataset. We address these limitations with GRAIL, introducing a paradigm shift in this domain. Instead of training a neural model to predict GED, GRAIL employs a novel combination of large language models (LLMs) and automated prompt tuning to generate a *program* that is used to compute GED. This shift from predicting GED to generating programs imparts various advantages, including end-to-end interpretability and an autonomous self-evolutionary learning mechanism without ground-truth supervision. Extensive experiments on seven datasets confirm that GRAIL not only surpasses state-of-the-art GED approximation methods in prediction quality but also achieves robust cross-domain generalization across diverse graph distributions.

Several applications call to align the nodes of two graphs in a way that minimizes a distance function.In practicality, the graphs to be aligned often have unequal orders (i.e., numbers of vertices) and no auxiliary labels or attributes; we refer to this problem as partial unlabeled graph alignment.Some proposals to address this problem add dummy nodes to the smaller graph to even the orders and align the ensuing graphs or employ embeddings such as GNNs, which yield ad hoc node representations.Unfortunately, as we show, an optimal solution to equal-order graph alignment using dummy nodes does not imply an optimal solution to partial graph alignment.To address this deficiency, in this paper, we propose Alpine, a Partial Unlabeled Graph Alignment algorithm that solely peruses the graphs' adjacency matrices, guided by a tailored objective function inspired by best-of-breed shape matching techniques and a state-ofthe-art optimization method.Extensive experiments demonstrate that Alpine consistently surpasses state-of-the-art graph alignment methods in solution quality across all benchmark datasets.

Graph Neural Networks (Gnns) have achieved remarkable success in various downstream tasks, such as node classification and link prediction. Yet, efficiently deploying Gnns remains a challenge due to their computational complexity. Graph knowledge distillation aims to address this by transferring task-specific structural knowledge from teacher Gnns to lightweight student Gnns or Multi-Layer Perceptrons (MLPs). Despite its promise, existing distillation approaches suffer from several limitations: (i) they require extensive task-specific supervision(ii) they must be retrained separately for each downstream task, and (iii) they often struggle in heterophilous settings. To overcome these challenges, we propose TAG2M, a Task-Agnostic Gnn-to-MLP distillation framework designed for efficient and accurate few-shot inference. TAG2M introduces several novel strategies, including a self-supervised contrastive loss that captures topological information solely from node attributes. Additionally, it leverages Lipschitz embeddings to encode positional information with provable distortion bounds, ensuring robust representation learning. To further enhance adaptability for few-shot inference, TAG2M incorporates a learnable prompt head, which facilitates rapid task adaptation even in label-scarce settings. Unlike prior methods, TAG2M generalizes well across both homophilous and heterophilous datasets while delivering a significant computational advantage, achieving up to a 20X -200X speed-up. Extensive evaluations on 11 public datasets demonstrate its superior accuracy across diverse tasks, including node classification, link prediction, and node regression, outperforming state-of-the-art approaches.

Graph Neural Networks (GNNs) are widely used for node classification, yet their opaque decision-making limits trust and adoption. While local explanations offer insights into individual predictions, global explanation methods—those that characterize an entire class—remain underdeveloped. Existing global explainers rely on motif discovery in small graphs, an approach that breaks down in large, real-world settings where subgraph repetition is rare, node attributes are high-dimensional, and predictions arise from complex structure-attribute interactions. We propose GnnXemplar, a novel global explainer inspired from Exemplar Theory from cognitive science. GnnXemplar identifies representative nodes in the GNN embedding space—exemplars—and explains predictions using natural language rules derived from their neighborhoods. Exemplar selection is framed as a coverage maximization problem over reverse $k$-nearest neighbors, for which we provide an efficient greedy approximation. To derive interpretable rules, we employ a self-refining prompt strategy using large language models (LLMs). Experiments across diverse benchmarks show that GnnXemplar significantly outperforms existing methods in fidelity, scalability, and human interpretability, as validated by a user study with 60 participants.

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this issue involves using counterfactual reasoning where the objective is to alter the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Toward this goal, we propose GCFExplainer , a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary . Extensive experiments on real graph datasets show that the global explanation from GCFExplainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage, a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers. We also demonstrate that GCFExplainer generates explanations that are more consistent with input dataset characteristics, and is robust under adversarial attacks. In addition, K-GCFExplainer , which incorporates a graph clustering component into GCFExplainer , is introduced as a more competitive extension for datasets with a clustering structure, leading to superior performance in three out of four datasets in the experiments and better scalability.

Neural networks (NNs) that exploit strong inductive biases based on physical laws and symmetries have shown remarkable success in learning the dynamics of physical systems directly from their trajectory. However, these works focus only on the systems that follow deterministic dynamics, such as Newtonian or Hamiltonian. Here, we propose a framework, namely Brownian graph neural networks (BroGNet), combining stochastic differential equations (SDEs) and GNNs to learn Brownian dynamics directly from the trajectory. We modify the architecture of BroGNet to enforce linear momentum conservation of the system, which, in turn, provides superior performance on learning dynamics as revealed empirically. We demonstrate this approach on several systems, namely, linear spring, linear spring with binary particle types, and non-linear spring systems, all following Brownian dynamics at finite temperatures. We show that BroGNet significantly outperforms proposed baselines across all the benchmarked Brownian systems. In addition, we demonstrate zero-shot generalizability of BroGNet to simulate unseen system sizes that are two orders of magnitude larger and to different temperatures than those used during training. Finally, we show that BroGNet conserves the momentum of the system resulting in superior performance and data efficiency. Altogether, our study contributes to advancing the understanding of the intricate dynamics of Brownian motion and demonstrates the effectiveness of graph neural networks in modeling such complex systems.

GNNs, like other deep learning models, are data and computation hungry. There is a pressing need to scale training of GNNs on large datasets to enable their usage on low-resource environments. Graph distillation is an effort in that direction with the aim to construct a smaller synthetic training set from the original training data without significantly compromising model performance. While initial efforts are promising, this work is motivated by two key observations: (1) Existing graph distillation algorithms themselves rely on training with the full dataset, which undermines the very premise of graph distillation. (2) The distillation process is specific to the target GNN architecture and hyper-parameters and thus not robust to changes in the modeling pipeline. We circumvent these limitations by designing a distillation algorithm called MIRAGE for graph classification. MIRAGE is built on the insight that a message-passing GNN decomposes the input graph into a multiset of computation trees. Furthermore, the frequency distribution of computation trees is often skewed in nature, enabling us to condense this data into a concise distilled summary. By compressing the computation data itself, as opposed to emulating gradient flows on the original training set—a prevalent approach to date—MIRAGE transforms into an unsupervised and architecture-agnostic distillation algorithm. Extensive benchmarking on real-world datasets underscores MIRAGE’s superiority, showcasing enhanced generalization accuracy, data compression, and distillation efficiency when compared to state-of-the-art baselines.

Numerous explainability methods have been proposed to shed light on the inner workings of GNNs. Despite the inclusion of empirical evaluations in all the proposed algorithms, the interrogative aspects of these evaluations lack diversity. As a result, various facets of explainability pertaining to GNNs, such as a comparative analysis of counterfactual reasoners, their stability to variational factors such as different GNN architectures, noise, stochasticity in non-convex loss surfaces, feasibility amidst domain constraints, and so forth, have yet to be formally investigated. Motivated by this need, we present a benchmarking study on perturbation-based explainability methods for GNNs, aiming to systematically evaluate and compare a wide range of explainability techniques. Among the key findings of our study, we identify the Pareto-optimal methods that exhibit superior efficacy and stability in the presence of noise. Nonetheless, our study reveals that all algorithms are affected by stability issues when faced with noisy data. Furthermore, we have established that the current generation of counterfactual explainers often fails to provide feasible recourses due to violations of topological constraints encoded by domain-specific considerations. Overall, this benchmarking study empowers stakeholders in the field of GNNs with a comprehensive understanding of the state-of-the-art explainability methods, potential research problems for further enhancement, and the implications of their application in real-world scenarios.

Graph partitioning aims to divide a graph into 𝑘 disjoint subsets while optimizing a specific partitioning objective.The majority of formulations related to graph partitioning exhibit NP-hardness due to their combinatorial nature.Conventional methods, like approximation algorithms or heuristics, are designed for distinct partitioning objectives and fail to achieve generalization across other important partitioning objectives.Recently machine learning-based methods have been developed that learn directly from data.Further, these methods have a distinct advantage of utilizing node features that carry additional information.However, these methods assume differentiability of target partitioning objective functions and cannot generalize for an unknown number of partitions, i.e., they assume the number of partitions is provided in advance.In this study, we develop NeuroCUT with two key innovations over previous methodologies.First, by leveraging a reinforcement learning-based framework over node representations derived from a graph neural network and positional features, NeuroCUT can accommodate any optimization objective, even those with non-differentiable functions.Second, we decouple the parameter space and the partition count making NeuroCUT inductive to any unseen number of partition, which is provided at query time.Through empirical evaluation, we demonstrate that NeuroCUT excels in identifying high-quality partitions, showcases strong generalization across a wide spectrum of partitioning objectives, and exhibits strong generalization to unseen partition count.

Instance-level explanation of graph neural networks (GNNs) is a well-studied area. These explainers, however, only explain an instance (e.g., a graph) and fail to uncover the combinatorial reasoning learned by a GNN from the training data towards making its predictions. In this work, we introduce GraphTrail, the first end-to-end, global, post-hoc GNN explainer that translates the functioning of a black-box GNN model to a boolean formula over the (sub)graph level concepts without relying on local explainers. GraphTrail is unique in automatically mining the discriminative subgraph-level concepts using Shapley values. Subsequently, the GNN predictions are mapped to a human-interpretable boolean formula over these concepts through symbolic regression. Extensive experiments across diverse datasets and GNN architectures demonstrate significant improvement over existing global explainers in mapping GNN predictions to faithful logical formulae. The robust and accurate performance of GraphTrail makes it invaluable for improving GNNs and facilitates adoption in domains with strict transparency requirements.

The necessity to align two graphs, minimizing a structural distance metric, is prevalent in biology, chemistry, recommender systems, and social network analysis. Due to the problem’s NP-hardness, prevailing graph alignment methods follow a modular and mediated approach, solving the problem by restricting to the domain of intermediary graph representations or products like embeddings, spectra, and graph signals. Restricting the problem to this intermediate space may distort the original problem and are hence predisposed to miss high-quality solutions. In this paper, we propose an unrestricted method, FUGAL, which finds a permutation matrix that maps one graph to another by directly operating on their adjacency matrices with judicious constraint relaxation. Extensive experimentation demonstrates that FUGAL consistently surpasses state-of-the-art graph alignment methods in accuracy across all benchmark datasets without encumbering efficiency.

Mixed Integer programs (MIPs) are typically solved by the Branch-and-Bound algorithm. Recently, Learning to imitate fast approximations of the expert strong branching heuristic has gained attention due to its success in reducing the running time for solving MIPs. However, existing learning-to-branch methods assume that the entire training data is available in a single session of training. This assumption is often not true, and if the training data is supplied in continual fashion over time, existing techniques suffer from catastrophic forgetting. In this work, we study the hitherto unexplored paradigm of Lifelong Learning to Branch on Mixed Integer Programs. To mitigate catastrophic forgetting, we propose LIMIP, which is powered by the idea of modeling an MIP instance in the form of a bipartite graph, which we map to an embedding space using a bipartite Graph Attention Network. This rich embedding space avoids catastrophic forgetting through the application of knowledge distillation and elastic weight consolidation, wherein we learn the parameters key towards retaining efficacy and are therefore protected from significant drift. We evaluate LIMIP on a series of NP-hard problems and establish that in comparison to existing baselines, LIMIP is up to 50% better when confronted with lifelong learning

Adversarial attacks on Graph Neural Networks (GNNs) reveal their security vulnerabilities, limiting their adoption in safety-critical applications. However, existing attack strategies rely on the knowledge of either the GNN model being used or the predictive task being attacked. Is this knowledge necessary? For example, a graph may be used for multiple downstream tasks unknown to a practical attacker. It is thus important to test the vulnerability of GNNs to adversarial perturbations in a model and task-agnostic setting. In this work, we study this problem and show that Gnns remain vulnerable even when the downstream task and model are unknown. The proposed algorithm, TANDIS (Targeted Attack via Neighborhood DIStortion) shows that distortion of node neighborhoods is effective in drastically compromising prediction performance. Although neighborhood distortion is an NP-hard problem, TANDIS designs an effective heuristic through a novel combination of Graph Isomorphism Network with deep Q-learning. Extensive experiments on real datasets show that, on average, TANDIS is up to 50% more effective than state-of-the-art techniques, while being more than 1000 times faster.

Optimization of atomic structures presents a challenging problem, due to their highly rough and non-convex energy landscape, with wide applications in the fields of drug design, materials discovery, and mechanics. Here, we present a graph reinforcement learning approach, StriderNet, that learns a policy to displace the atoms towards low energy configurations. We evaluate the performance of StriderNet on three complex atomic systems, namely, binary Lennard-Jones particles, calcium silicate hydrates gel, and disordered silicon. We show that StriderNet outperforms all classical optimization algorithms and enables the discovery of a lower energy minimum. In addition, StriderNet exhibits a higher rate of reaching minima with energies, as confirmed by the average over multiple realizations. Finally, we show that StriderNet exhibits inductivity to unseen system sizes that are an order of magnitude different from the training system. All the codes and datasets are available at https://github.com/M3RG-IITD/StriderNET.

Graph neural networks (GNNs), in general, are built on the assumption of a static set of features characterizing each node in a graph. This assumption is often violated in practice. Existing methods partly address this issue through feature imputation. However, these techniques (i) assume uniformity of feature set across nodes, (ii) are transductive by nature, and (iii) fail to work when features are added or removed over time. In this work, we address these limitations through a novel GNN framework called GRAFENNE. GRAFENNE performs a novel allotropic transformation on the original graph, wherein the nodes and features are decoupled through a bipartite encoding. Through a carefully chosen message passing framework on the allotropic transformation, we make the model parameter size independent of the number of features and thereby inductive to both unseen nodes and features. We prove that GRAFENNE is at least as expressive as any of the existing message-passing GNNs in terms of Weisfeiler-Leman tests, and therefore, the additional inductivity to unseen features does not come at the cost of expressivity. In addition, as demonstrated over four real-world graphs, GRAFENNE empowers the underlying GNN with high empirical efficacy and the ability to learn in continual fashion over streaming feature sets.

Modelling spatio-temporal processes on road networks is a task of growing importance. While significant progress has been made on developing spatio-temporal graph neural networks (Gnns), existing works are built upon three assumptions that are not practical on real-world road networks. First, they assume sensing on every node of a road network. In reality, due to budget-constraints or sensor failures, all locations (nodes) may not be equipped with sensors. Second, they assume that sensing history is available at all installed sensors. This is unrealistic as well due to sensor failures, loss of packets during communication, etc. Finally, there is an assumption of static road networks. Connectivity within networks change due to road closures, constructions of new roads, etc. In this work, we develop Frigate to address all these shortcomings. Frigate is powered by a spatio-temporal Gnn that integrates positional, topological, and temporal information into rich inductive node representations. The joint fusion of this diverse information is made feasible through a novel combination of gated Lipschitz embeddings with Lstms. We prove that the proposed Gnn architecture is provably more expressive than message-passing Gnns used in state-of-the-art algorithms. The higher expressivity of Frigate naturally translates to superior empirical performance conducted on real-world network-constrained traffic data. In addition, Frigate is robust to frugal sensor deployment, changes in road network connectivity, and temporal irregularity in sensing.

Air pollution poses serious health concerns in developing countries, such as India, necessitating large-scale measurement for correlation analysis, policy recommendations, and informed decision-making. However, fine-grained data collection is costly. Specifically, static sensors for pollution measurement cost several thousand dollars per unit, leading to inadequate deployment and coverage. To complement the existing sparse static sensor network, we propose a mobile sensor network utilizing lower-cost PM2.5 sensors mounted on public buses in the Delhi-NCR region of India. Through this exercise, we introduce a novel dataset AirDelhi comprising PM2.5 and PM10 measurements. This dataset is made publicly available, at https://www.cse.iitd.ac.in/pollutiondata, serving as a valuable resource for machine learning (ML) researchers and environmentalists. We present three key contributions with the release of this dataset. Firstly, through in-depth statistical analysis, we demonstrate that the released dataset significantly differs from existing pollution datasets, highlighting its uniqueness and potential for new insights. Secondly, the dataset quality been validated against existing expensive sensors. Thirdly, we conduct a benchmarking exercise (https://github.com/sachin-iitd/DelhiPMDatasetBenchmark), evaluating state-of-the-art methods for interpolation, feature imputation, and forecasting on this dataset, which is the largest publicly available PM dataset to date. The results of the benchmarking exercise underscore the substantial disparities in accuracy between the proposed dataset and other publicly available datasets. This finding highlights the complexity and richness of our dataset, emphasizing its value for advancing research in the field of air pollution.

Influence maximization (IM) refers to the problem of finding a subset of nodes in a network through which we could maximize our reach to other nodes in the network. This set is often called the "seed set", and its constituent nodes maximize the social diffusion process. IM has previously been studied in various settings, including under a time deadline, subject to constraints such as that of budget or coverage, and even subject to measures other than the centrality of nodes. The solution approach has generally been to prove that the objective function is submodular, or has a submodular proxy, and thus has a close greedy approximation. In this paper, we explore a variant of the IM problem where we wish to reach out to and maximize the probability of infection of a small subset of bounded capacity K. We show that this problem does not exhibit the same submodular guarantees as the original IM problem, for which we resort to the theory of gamma-weakly submodular functions. Subsequently, we develop a greedy algorithm that maximizes our objective despite the lack of submodularity. We also develop a suitable learning model that out-competes baselines on the task of predicting the top-K infected nodes, given a seed set as input.

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this is counterfactual reasoning where the objective is to change the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Towards this goal, we propose GCFExplainer, a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary. Extensive experiments on real graph datasets show that the global explanation from GCFExplainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage and a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers.

Social commerce platforms are emerging businesses where producers sell products through re-sellers who advertise the products to other customers in their social network. Due to the increasing popularity of this business model, thousands of small producers and re-sellers are starting to depend on these platforms for their livelihood; thus, it is important to provide fair earning opportunities to them. The enormous product space in such platforms prohibits manual search, and motivates the need for recommendation algorithms to effectively allocate product exposure and, consequently, earning opportunities. In this work, we focus on the fairness of such allocations in social commerce platforms and formulate the problem of assigning products to re-sellers as a fair division problem with indivisible items under two-sided cardinality constraints, wherein each product must be given to at least a certain number of re-sellers and each re-seller must get a certain number of products.

There has been a recent surge in learning generative models for graphs. While impressive progress has been made on static graphs, work on generative modeling of temporal graphs is at a nascent stage with significant scope for improvement. First, existing generative models do not scale with either the time horizon or the number of nodes. Second, existing techniques are transductive in nature and thus do not facilitate knowledge transfer. Finally, due to relying on one-to-one node mapping from source to the generated graph, existing models leak node identity information and do not allow up-scaling/down-scaling the source graph size. In this paper, we bridge these gaps with a novel generative model called TIGGER. TIGGER derives its power through a combination of temporal point processes with auto-regressive modeling enabling both transductive and inductive variants. Through extensive experiments on real datasets, we establish TIGGER generates graphs of superior fidelity, while also being up to 3 orders of magnitude faster than the state-of-the-art.

Along with the rapid growth and rise to prominence of food delivery platforms, concerns have also risen about the terms of employment of the ``gig workers'' underpinning this growth. Our analysis on data derived from a real-world food delivery platform across three large cities from India show that there is significant inequality in the money delivery agents earn. In this paper, we formulate the problem of fair income distribution among agents while also ensuring timely food delivery. We establish that the problem is not only NP-hard but also inapproximable in polynomial time. We overcome this computational bottleneck through a novel matching algorithm called FairFoody. Extensive experiments over real-world food delivery datasets show FairFoody imparts up to 10 times improvement in equitable income distribution when compared to baseline strategies, while also ensuring minimal impact on customer experience.

With the increasing popularity of food delivery platforms, it has become pertinent to look into the working conditions of the `gig' workers in these platforms, especially providing them fair wages, reasonable working hours, and transparency on work availability. However, any solution to these problems must not degrade customer experience and be cost-effective to ensure that platforms are willing to adopt them. We propose Work4Food, which provides income guarantees to delivery agents, while minimizing platform costs and ensuring customer satisfaction. Work4Food ensures that the income guarantees are met in such a way that it does not lead to increased working hours or degrade environmental impact. To incorporate these objectives, Work4Food balances supply and demand by controlling the number of agents in the system and providing dynamic payment guarantees to agents based on factors such as agent location, ratings, etc. We evaluate Work4Food on a real-world dataset from a leading food delivery platform and establish its advantages over the state of the art in terms of the multi-dimensional objectives at hand.

Lagrangian and Hamiltonian neural networks LNN and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited to simple systems such as pendulums and springs or a single rigid body such as a gyroscope or a rigid rotor. Here, we present a Lagrangian graph neural network (LGNN) that can learn the dynamics of articulated rigid bodies by exploiting their topology. We demonstrate the performance of LGNN by learning the dynamics of ropes, chains, and trusses with the bars modeled as rigid bodies. LGNN also exhibits generalizability---LGNN trained on chains with a few segments exhibits generalizability to simulate a chain with large number of links and arbitrary link length. We also show that the LGNN can simulate unseen hybrid systems including bars and chains, on which they have not been trained on. Specifically, we show that the LGNN can be used to model the dynamics of complex real-world structures such as the stability of tensegrity structures. Finally, we discuss the non-diagonal nature of the mass matrix and its ability to generalize in complex systems.

Similarity search in graph databases is one of the most fundamental operations in graph analytics. Among various distance functions, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this computational bottleneck, neural approaches to learn and predict edit distance in polynomial time have received much interest. While considerable progress has been made, there exist limitations that need to be addressed. First, the efficacy of an approximate distance function lies not only in its approximation accuracy, but also in the preservation of its properties. To elaborate, although GED is a metric, its neural approximations do not provide such a guarantee. This prohibits their usage in higher order tasks that rely on metric distance functions, such as clustering or indexing. Second, several existing frameworks for GED do not extend to SED due to SED being asymmetric. In this work, we design a novel siamese graph neural network called Greed, which through a carefully crafted inductive bias, learns GED and SED in a property-preserving manner. Through extensive experiments across $10$ real graph datasets containing up to $7$ million edges, we establish that Greed is not only more accurate than the state of the art, but also up to $3$ orders of magnitude faster. Even more significantly, due to preserving the triangle inequality, the generated embeddings are indexable and consequently, even in a CPU-only environment, Greed is up to $50$ times faster than GPU-powered computations of the closest baseline.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. Then, we evaluate them on spring, pendulum, and gravitational and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

Given a stream of food orders and available delivery vehicles, how should orders be assigned to vehicles so that the delivery time is minimized? For a successful assignment strategy, two key decisions need to be made: (1) assignment of orders to vehicles, (2) grouping orders into batches to cope with limited vehicle availability. We show that the minimization problem is not only NP-hard but inapproximable in polynomial time. To mitigate this computational bottleneck, we develop an algorithm called FOODMATCH, which maps the vehicle assignment problem to that of minimum weight perfect matching on a bipartite graph. The solution quality is further enhanced by reducing batching to a graph clustering problem. Extensive experiments on food-delivery data from large metropolitan cities establish that FOODMATCH is substantially better than baseline strategies on a number of metrics.

Majority of the existing graph neural networks(GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods map to similar embeddings in those networks. This limitation prevents accurate performance in predictive tasks that rely on position information. In this paper, we develop GRAPHREACH , a position-aware inductive GNN that captures the global positions of nodes through reachability estimations with respect to a set of anchor nodes. The anchors are strategically selected so that reachability estimations across all the nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and, consequently, develop a greedy (1−1/e) approximation heuristic. Empirical evaluation against state-of-the-art GNN architectures reveal that GRAPHREACH provides up to 40% relative improvement in accuracy. In addition, it is more robust to adversarial attacks.

Predicting the most likely route from a source location to a destination is a core functionality in mapping services. Although the problem has been studied in the literature, two key limitations remain to be addressed. First, our study reveals that a significant portion of the routes recommended by existing methods fail to reach the destination. Second, existing techniques are transductive in nature; hence, they fail to recommend routes if unseen roads are encountered at inference time. In this paper, we address these limitations through an inductive algorithm called NeuroMLR. NeuroMLR learns a generative model from historical trajectories by conditioning on three explanatory factors: the current location, the destination, and real-time traffic conditions. The conditional distributions are learned through a novel combination of Lipschitz embedding with Graph Convolutional Networks (GCN) using historical trajectory data. Through in-depth experiments on real-world datasets, we establish that NeuroMLR imparts significant improvement in accuracy over the state of the art. More importantly, NeuroMLR generalizes dramatically better to unseen data and the recommended routes reach the destination with much higher likelihood than existing techniques.

In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices can be partitioned into two subsets with negative edges present only across the partitions. Balanced portions of a graph have been shown to increase coherence among its members and lead to better performance. While existing works have focused primarily on finding the largest balanced subgraph inside a graph, we study the network design problem of maximizing balance of a target community (subgraph). In particular, given a budget b and a community of interest within the signed network, we aim to make the community as close to being balanced as possible by deleting up to b edges. Besides establishing NP-hardness, we also show that the problem is non-monotone and non-submodular. To overcome these computational challenges, we propose heuristics based on the spectral relation of balance with the Laplacian spectrum of the network. Since the spectral approach lacks approximation guarantees, we further design a greedy algorithm, and its randomized version, with provable bounds on the approximation quality. The bounds are derived by exploiting pseudo-submodularity of the balance maximization function. Empirical evaluation on eight real-world signed networks establishes that the proposed algorithms are effective, efficient, and scalable to graphs with millions of edges.

Regular simple path query (RPQ) is one of the fundamental operators in graph analytics. In an RPQ, the input is a graph, a source node and a regular expression. The goal is to identify all nodes that are connected to the source through a simple path whose label sequence satisfies the given regular expression. The regular expression acts as a formal specification of the search space that is of interest to the user. Although regular expressions have high expressive power, they act as barrier to non-technical users. Furthermore, to fully realize the power of regular expressions, the user must be familiar with the domain of the graph dataset. In this study, we address this bottleneck by bridging RPQs with the query-by-example paradigm. More specifically, we ask the user for an exemplar pair that characterizes the paths of interest, and the regular expression is automatically inferred from this exemplar. This novel problem introduces several new challenges. How do we infer the regex? Given that answering RPQs is NP-hard, how do we scale to large graphs? We address these challenges through a unique combination of Biermann and Feldman's algorithm with NFA-guided random walks with restarts. Extensive experiments on multiple real, million-scale datasets establish that RQuBE is at least 3 orders of magnitude faster than baseline strategies with an average accuracy in excess of 90%.

There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of a budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node. To further facilitate the combinatorial nature of the problem, GCOMB utilizes a Q-learning framework, which is made efficient through importance sampling. We perform extensive experiments on real graphs to benchmark the efficiency and efficacy of GCOMB. Our results establish that GCOMB is 100 times faster and marginally better in quality than state-of-the-art algorithms for learning combinatorial algorithms. Additionally, a case-study on the practical combinatorial problem of Influence Maximization (IM) shows GCOMB is 150 times faster than the specialized IM algorithm IMM with similar quality.

Graph generative models have been extensively studied in the data mining literature. While traditional techniques are based on generating structures that adhere to a pre-decided distribution, recent techniques have shifted towards learning this distribution directly from the data. While learning-based approaches have imparted significant improvement in quality, some limitations remain to be addressed. First, learning graph distributions introduces additional computational overhead, which limits their scalability to large graph databases. Second, many techniques only learn the structure and do not address the need to also learn node and edge labels, which encode important semantic information and influence the structure itself. Third, existing techniques often incorporate domain-specific rules and lack generalizability. Fourth, the experimentation of existing techniques is not comprehensive enough due to either using weak evaluation metrics or focusing primarily on synthetic or small datasets. In this work, we develop a domain-agnostic technique called GraphGen to overcome all of these limitations. GraphGen converts graphs to sequences using minimum DFS codes. Minimum DFS codes are canonical labels and capture the graph structure precisely along with the label information. The complex joint distributions between structure and semantic labels are learned through a novel LSTM architecture. Extensive experiments on million-sized, real graph datasets show GraphGen to be 4 times faster on average than state-of-the-art techniques while being significantly better in quality across a comprehensive set of 11 different metrics. Our code is released at: https://github.com/idea-iitd/graphgen.

We investigate the problem of correlated subgraphs mining (CSM) where the goal is to identify pairs of subgraph patterns that frequently co-occur in proximity within a single graph. Correlated subgraph patterns are different from frequent subgraphs due to the flexibility in connections between constituent subgraph instances and thus, existing frequent subgraphs mining algorithms cannot be directly applied for CSM. Moreover, computing the degree of correlation between two patterns requires enumerating and finding distances between every pair of subgraph instances of both patterns - a task that is both memory-intensive as well as computationally demanding. To this end, we propose two holistic best-first exploration algorithms: CSM-E (an exact method) and CSM-A (a more efficient approximate method with near-optimal quality). To further improve efficiency, we propose a top- k pruning strategy, while to reduce memory footprint, we develop a compressed data structure called R eplica, which stores all instances of a subgraph pattern on demand. Our empirical results demonstrate that the proposed algorithms not only mine interesting correlations, but also achieve good scalability over large networks.

Several services today are annotated with points of interest (PoIs) such as "coffee shop", "park", etc. In this paper, we study the query where a user provides a set of relevant PoIs and wants to identify the optimal route covering these PoIs. Ideally, the route should be small in length so that the user can conveniently explore the PoIs. On the other hand, the route should cover as many of the input PoIs as possible. These conflicting requirements of the optimal route raise an intriguing question: how do you balance the importance of route length vs. PoI coverage? If the route is to be covered on foot, and it is raining, length is critical for convenience. On the other hand, if the weather conditions are good, or the user is equipped with a vehicle, coverage is more important. In essence, the relative importance depends on several latent factors and we solve this dilemma through skyline route queries. Skyline routes subsume the choice of the optimization function for a route since the optimal route for any rational user is necessarily a part of the skyline set. Our analysis reveals that the problem is NP-hard. We overcome this bottleneck by designing an algorithm called SkyRoute. SkyRoute drastically prunes the search space through a goal-directed search, which is further empowered by Lipschitz embedding, and provides up to 4 orders of magnitude speed-up over baseline techniques.

A fundamental query in labeled graphs is to determine if there exists a path between a given source and target vertices, such that the path satisfies a given label constraint. One of the powerful forms of specifying label constraints is through regular expressions, and the resulting problem of reachability queries under regular simple paths (RSP) form the core of many practical graph query languages such as SPARQL from W3C, Cypher of Neo4J, Oracle's PGQL and LDBC's G-CORE. Despite its importance, since it is known that answering RSP queries is NP-Hard, there are no scalable and practical solutions for answering reachability with full-range of regular expressions as constraints. In this paper, we circumvent this computational bottleneck by designing a random-walk based sampling algorithm called ARRIVAL, which is backed by theoretical guarantees on its expected quality. Extensive experiments on billion-sized real graph datasets with thousands of labels show that ARRIVAL to be 100 times faster than baseline strategies with an average accuracy of 95%.

The phenomenal growth of graph data from a wide variety of real-world applications has rendered graph querying to be a problem of paramount importance. Traditional techniques use structural as well as node similarities to find matches of a given query graph in a (large) target graph. However, almost all existing techniques have tacitly ignored the presence of relationships in graphs, which are usually encoded through interactions between node and edge labels. In this paper, we propose RAQ-Relationship-Aware Graph Querying-to mitigate this gap. Given a query graph, RAQ identifies the k best matching subgraphs of the target graph that encode similar relationships as in the query graph. To assess the utility of RAQ as a graph querying paradigm for knowledge discovery and exploration tasks, we perform a user survey on the Internet Movie Database (IMDb), where an overwhelming 86% of the 170 surveyed users preferred the relationship-aware match over traditional graph querying. The need to perform subgraph isomorphism renders RAQ NP-hard. The querying is made practical through beam stack search. Extensive experiments on multiple real-world graph datasets demonstrate RAQ to be effective, efficient, and scalable.

In taxi ride-sharing, multiple customers are allotted to the same taxi as long as they are compatible, i.e., if none of them suffers a detour beyond a permissible threshold. To attract customers to ride-sharing, taxi operators promise a reduced fare upfront. As a result, if the taxi fails to pair the initial customer with additional compatible passengers, the taxi operator incurs a financial loss. Hence, it is important to ensure that the taxi finds compatible customers once it has picked up the initial customer. In the current scenario, the appearance of subsequent compatible customers is left to luck: a taxi moves along the shortest (or quickest) path for the existing customer and hopes to find additional compatible customers on its way. In this paper, we ask: Is the shortest path the optimal path for ride-sharing? To investigate this question, we develop a route recommendation algorithm called Share, which predicts the route with the highest probability of finding compatible customers, while staying within the detour limits. Through extensive evaluations on real datasets, we show that Share reduces failure rate in ride-sharing by up to 40%, while also improving waiting time for customers by 20%. Technically, the route recommendation problem is NP-hard. We overcome this bottleneck, by reducing the search space of the entire road network into a smaller directed acyclic graph, on which we perform dynamic programming to identify the optimal route. This strategy allows us to answer queries within 0.2 seconds, and thereby making Share deployable on real road conditions.

We study the problem of route recommendation to idle taxi drivers such that the distance between the taxi and an anticipated customer request is minimized. Minimizing the distance to the next anticipated customer leads to more productivity for the taxi driver and less waiting time for the customer. To anticipate when and where future customer requests are likely to come from and accordingly recom- mend routes, we develop a route recommendation engine called MDM: Minimizing Distance through Monte Carlo Tree Search. In contrast to existing techniques, MDM employs a continuous learning platform where the underlying model to predict future customer requests is dynamically updated. Extensive experiments on real taxi data from New York and San Francisco reveal that MDM is up to 70% better than the state of the art and robust to anomalous events such as concerts, sporting events, etc.

In several domains, the flow of data is governed by an underlying network. Reduction of delays in end-to-end data flow is an important network optimization task. Reduced delays enable shorter travel times for vehicles in road networks, faster information flow in social networks, and increased rate of packets in communication networks. While techniques for network delay minimization have been proposed, they fail to provide any noticeable reduction in individual data flows. Furthermore, they treat all nodes as equally important, which is often not the case in real-world networks. In this paper, we incorporate these practical aspects and propose a network design problem where the goal is to perform k network upgrades such that it maximizes the number of flows in the network with a noticeable reduction in delay. We show that the problem is NP-hard, APX-hard, and non-submodular. We overcome these computational challenges by designing an importance sampling based algorithm with provable quality guarantees. Through extensive experiments on real and synthetic data sets, we establish that importance sampling imparts up to 1000 times speed-up over the greedy approach, and provides up to 70 times the improvement achieved by the state-of-the-art technique.

A search query, being a very concise grounding of user intent, could potentially have many possible interpretations. Search engines hedge their bets by diversifying top results to cover multiple such possibilities so that the user is likely to be satisfied, whatever be her intended interpretation. Diversified Query Expansion is the problem of diversifying query expansion suggestions, so that the user can specialize the query to better suit her intent, even before perusing search results. In this paper, we consider the usage of semantic resources and tools to arrive at improved methods for diversified query expansion. In particular, we develop two methods, those that leverage Wikipedia and pre-learnt distributional word embeddings respectively. Both the approaches operate on a common three-phase framework; that of first taking a set of informative terms from the search results of the initial query, then building a graph, following by using a diversity-conscious node ranking to prioritize candidate terms for diversified query expansion. Our methods differ in the second phase, with the first method Select-Link-Rank (SLR) linking terms with Wikipedia entities to accomplish graph construction; on the other hand, our second method, Select-Embed-Rank (SER), constructs the graph using similarities between distributional word embeddings. Through an empirical analysis and user study, we show that SLR ourperforms state-of-the-art diversified query expansion methods, thus establishing that Wikipedia is an effective resource to aid diversified query expansion. Our empirical analysis also illustrates that SER outperforms the baselines convincingly, asserting that it is the best available method for those cases where SLR is not applicable; these include narrow-focus search systems where a relevant knowledge base is unavailable. Our SLR method is also seen to outperform a state-of-the-art method in the task of diversified entity ranking.

Optimal location queries identify the best locations to set up new facilities for providing service to its users. For several businesses such as fuel stations, cellphone base-stations, etc., placement queries require taking into account the mobility patterns (or trajectories) of the users. In this work, we formulate the TOPS (Trajectory-Aware Optimal Placement of Services) query that locates the best k sites on a road network for the prevailing user trajectories. The problem is NP-hard. The greedy approach, which is the state-of-the-art technique for this problem, is not scalable and practical for real urban-scale scenarios, primarily due to its high memory footprint beyond the capabilities of commodity machines. To overcome these challenges, we develop an indexing framework called NETCLUS that derives its power through an unique combination of FM sketches with network clustering. Empirical studies show that NETCLUS requires less than 100 s to answer the TOPS query on real datasets comprising of more than 250,000 sites and 120,000 trajectories.

Influence maximization (IM) on social networks is one of the most active areas of research in computer science. While various IM techniques proposed over the last decade have definitely enriched the field, unfortunately, experimental reports on existing techniques fall short in validity and integrity since many comparisons are not based on a common platform or merely discussed in theory. In this paper, we perform an in-depth benchmarking study of IM techniques on social networks. Specifically, we design a benchmarking platform, which enables us to evaluate and compare the existing techniques systematically and thoroughly under identical experimental conditions. Our benchmarking results analyze and diagnose the inherent deficiencies of the existing approaches and surface the open challenges in IM even after a decade of research. More fundamentally, we unearth and debunk a series of myths and establish that there is no single state-of-the-art technique in IM. At best, a technique is the state of the art in only one aspect.

MOTIVATION: The ability to predict pathways for biosynthesis of metabolites is very important in metabolic engineering. It is possible to mine the repertoire of biochemical transformations from reaction databases, and apply the knowledge to predict reactions to synthesize new molecules. However, this usually involves a careful understanding of the mechanism and the knowledge of the exact bonds being created and broken. There is a need for a method to rapidly predict reactions for synthesizing new molecules, which relies only on the structures of the molecules, without demanding additional information such as thermodynamics or hand-curated reactant mapping, which are often hard to obtain accurately. RESULTS: We here describe a robust method based on subgraph mining, to predict a series of biochemical transformations, which can convert between two (even previously unseen) molecules. We first describe a reliable method based on subgraph edit distance to map reactants and products, using only their chemical structures. Having mapped reactants and products, we identify the reaction centre and its neighbourhood, the reaction signature, and store this in a reaction rule network. This novel representation enables us to rapidly predict pathways, even between previously unseen molecules. We demonstrate this ability by predicting pathways to molecules not present in the KEGG database. We also propose a heuristic that predominantly recovers natural biosynthetic pathways from amongst hundreds of possible alternatives, through a directed search of the reaction rule network, enabling us to provide a reliable ranking of the different pathways. Our approach scales well, even to databases with >100 000 reactions. AVAILABILITY AND IMPLEMENTATION: A Java-based implementation of our algorithms is available at https://github.com/RamanLab/ReactionMiner. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Several services today are annotated with points of interest (PoIs) such as "coffee shop", "park", etc. A region of interest (RoI) is a neighborhood that contains PoIs relevant to the user. In this paper, we study the scenario where a user wants to identify the best RoI in a city. The user expresses relevance through a set of keywords denoting PoIs. Ideally, the RoI should be small enough in size such that the user can conveniently explore the PoIs. On the other hand, it should be as relevant as possible. How does one balance the importance of size versus relevance? To a user exploring the RoI on foot, size is more critical. However, for a user equipped with a vehicle, relevance is a more important factor. In this paper, we solve this dilemma through skyline subgraph queries on keyword-embedded road networks. Skyline subgraphs subsume the choice of optimization function for an RoI since the optimal RoI for any rational user is necessarily a part of the skyline set. Our analysis reveals that the problem of computing the skyline set is NP-hard. We overcome the computational bottleneck by proposing a polynomial-time approximation algorithm called SkyGraph. To further expedite the running time, we develop an index structure, Partner Index , that drastically prunes the search space and provides up to 3 orders of magnitude speed-up on real road networks over the baseline approach. The datasets and executables are available at http://www.cse.iitd.ac.in/~sayan/software.html.

Mining subgraph patterns is an active area of research. Existing research has primarily focused on mining all subgraph patterns in the database. However, due to the exponential subgraph search space, the number of patterns mined, typically, is too large for any human mediated analysis. Consequently, deriving insights from the mined patterns is hard for domain scientists. In addition, subgraph pattern mining is posed in multiple forms: the function that models if a subgraph is a pattern varies based on the application and the database could be over multiple graphs or a single, large graph. In this paper, we ask the following question: Given a subgraph importance function and a budget k, which are the k subgraph patterns that best represent all other patterns of interest? We show that the problem is NP-hard, and propose a generic framework called RESLING that adapts to arbitrary subgraph importance functions and generalizable to both transactional graph databases as well as single, large graphs. Experiments show that RESLING is up to 20 times more representative of the pattern space and 2 orders of magnitude faster than the state-of-the-art techniques. The executables for the tool are available at http://www.cse.iitm.ac.in/~sayan/software.html.

In this paper, we study the problem of mining temporally anomalous sub-trajectory patterns from an input trajectory in a scalable manner. Given the prevailing road conditions, a sub-trajectory is temporally anomalous if its travel time deviates significantly from the expected time. Mining these patterns requires us to delve into the sub-trajectory space, which is not scalable for real-time analytics. To overcome this scalability challenge, we design a technique called MANTRA. We study the properties unique to anomalous sub-trajectories and utilize them in MANTRA to iteratively refine the search space into a disjoint set of sub-trajectory islands. The expensive enumeration of all possible sub-trajectories is performed only on the islands to compute the answer set of maximal anomalous sub-trajectories. Extensive experiments on both real and synthetic datasets establish MANTRA as more than 3 orders of magnitude faster than baseline techniques. Moreover, through trajectory classification and segmentation, we demonstrate that the proposed model conforms to human intuition.

Quantifying the similarity between two trajectories is a fundamental operation in analysis of spatio-temporal databases. While a number of distance functions exist, the recent shift in the dynamics of the trajectory generation procedure violates one of their core assumptions; a consistent and uniform sampling rate. In this paper, we formulate a robust distance function called Edit Distance with Projections (EDwP) to match trajectories under inconsistent and variable sampling rates through dynamic interpolation. This is achieved by deploying the idea of projections that goes beyond matching only the sampled points while aligning trajectories. To enable efficient trajectory retrievals using EDwP, we design an index structure called TrajTree. TrajTree derives its pruning power by employing the unique combination of bounding boxes with Lipschitz embedding. Extensive experiments on real trajectory databases demonstrate EDwP to be up to 5 times more accurate than the state-of-the-art distance functions. Additionally, TrajTree increases the efficiency of trajectory retrievals by up to an order of magnitude over existing techniques.

In this paper, we develop an algorithm to cluster places not only based on their locations but also their semantics. Specifically, two places are considered similar if they are spatially close and visited by people of similar communities. With the explosion in the availability of location-tracking technologies, it has become easy to track locations and movements of users through user "check-ins". These check-ins provide insights into the community structure of people visiting a place, which is leveraged and integrated into the proposed geo-social clustering framework called GeoScop. While community detection is typically done on social networks, in our problem, we lack any network data. Rather, two people belong to the same community if they visit similar geo-social clusters. We tackle this chicken-and-egg problem through an iterative procedure of expectation maximization and DBSCAN. Extensive experiments on real check-in data demonstrate that GeoScop mines semantically meaningful clusters that cannot be found by using any of the existing clustering techniques. Furthermore, GeoScop is up to 6 times more pure in social quality than the state-of-the-art technique. The executables for the tool are available at http://www.cse.iitm.ac.in/ ~simsayan/software.html.

We handle the problem of efficient user-mobility driven macro-cell planning in cellular networks. As cellular networks embrace heterogeneous technologies (including long range 3G/4G and short range WiFi, Femto-cells, etc.), most traffic generated by static users gets absorbed by the short-range technologies, thereby increasingly leaving mobile user traffic to macro-cells. To this end, we consider a novel approach that factors in the trajectories of mobile users as well as the impact of city geographies and their associated road networks for macro-cell planning. Given a budget k of base-stations that can be upgraded, our approach selects a deployment that improves the most number of user trajectories. The generic formulation incorporates the notion of quality of service of a user trajectory as a parameter to allow different application-specific requirements, and operator choices. We show that the proposed trajectory utility maximization problem is NP-hard, and design multiple heuristics. We evaluate our algorithms with real and synthetic datasets emulating different city geographies to demonstrate their efficacy. For instance, with an upgrade budget k of 20%, our algorithms perform 3-8 times better in improving the user quality of service on trajectories when compared to greedy location-based base-station upgrades.

A fundamental problem in behavioral analysis of human interactions is to understand how communications unfold. In this paper, we study this problem by mining Communication motifs from dynamic interaction networks. A communication motif is a recurring subgraph that has a similar sequence of information flow. Mining communication motifs requires us to explore the exponential subgraph search space where existing techniques fail to scale. To tackle this scalability bottleneck, we develop a technique called COMMIT. COMMIT converts a dynamic graph into a database of sequences. Through careful analysis in the sequence space, only a small portion of the exponential search space is accessed to identify regions embedding communication motifs. Extensive experiments on three different social networks show COMMIT to be up to two orders of magnitude faster than baseline techniques. Furthermore, qualitative analysis demonstrate communication motifs to be effective in characterizing the recurring patterns of interactions while also revealing the role that the underlying social network plays in shaping human behavior.

The explosion in the availability of GPS-enabled devices has resulted in an abundance of trajectory data. In reality, however, majority of these trajectories are collected at a low sampling rate and only provide partial observations on their actually traversed routes. Consequently, they are mired with uncertainty. In this paper, we develop a technique called Infer Tra to infer uncertain trajectories from network-constrained partial observations. Rather than predicting the most likely route, the inferred uncertain trajectory takes the form of an edge-weighted graph and summarizes all probable routes in a holistic manner. For trajectory inference, Infer Tra employs Gibbs sampling by learning a Network Mobility Model (NMM) from a database of historical trajectories. Extensive experiments on real trajectory databases show that the graph-based approach of Infer Tra is up to 50% more accurate, 20 times faster, and immensely more versatile than state-of-the-art techniques.

Given a function that classifies a data object as relevant or irrelevant, we consider the task of selecting k objects that best represent all relevant objects in the underlying database. This problem occurs naturally when analysts want to familiarize themselves with the relevant objects in a database using a small set of k exemplars. In this paper, we solve the problem of top-k representative queries on graph databases. While graph databases model a wide range of scientific data, solving the problem in the context of graphs presents us with unique challenges due to the inherent complexity of matching structures. Furthermore, top-k representative queries map to the classic Set Cover problem, making it NP-hard. To overcome these challenges, we develop a greedy approximation with theoretical guarantees on the quality of the answer set, noting that a better approximation is not feasible in polynomial time. To further optimize the quadratic computational cost of the greedy algorithm, we propose an index structure called NB-Index to index the \theta-neighborhoods of the database graphs by employing a novel combination of Lipschitz embedding and agglomerative clustering. Extensive experiments on real graph datasets validate the efficiency and effectiveness of the proposed techniques that achieve up to two orders of magnitude speed-up over state-of-the-art algorithms.

Global-state networks provide a powerful mechanism to model the increasing heterogeneity in data generated by current systems. Such a network comprises of a series of network snapshots with dynamic local states at nodes, and a global network state indicating the occurrence of an event. Mining discriminative subgraphs from global-state networks allows us to identify the influential sub-networks that have maximum impact on the global state and unearth the complex relationships between the local entities of a network and their collective behavior. In this paper, we explore this problem and design a technique called MINDS to mine minimally discriminative subgraphs from large global-state networks. To combat the exponential subgraph search space, we derive the concept of an edit map and perform Metropolis Hastings sampling on it to compute the answer set. Furthermore, we formulate the idea of network-constrained decision trees to learn prediction models that adhere to the underlying network structure. Extensive experiments on real datasets demonstrate excellent accuracy in terms of prediction quality. Additionally, MINDS achieves a speed-up of at least four orders of magnitude over baseline techniques.

Increased availability of large repositories of chemical compounds has created new challenges and opportunities for the application of data-mining and indexing techniques to problems in chemical informatics. The primary goal in analysis of molecular databases is to identify structural patterns that can predict biological activity. Two of the most popular approaches to representing molecular topologies are graphs and 3D geometries. As a result, the problem of indexing and mining structural patterns map to indexing and mining patterns from graph and 3D geometric databases.

Content sharing in social networks is a powerful mechanism for discovering content on the Internet. The degree to which content is disseminated within the network depends on the connectivity relationships among network nodes. Existing schemes for recommending connections in social networks are based on the number of common neighbors, similarity of user profiles, etc. However, such similarity-based connections do not consider the amount of content discovered.

In this paper, we formulate a top-kquery that compares objects in a database to a user-provided query object on a novel scoring function. The proposed scoring function combines the idea ofattractiveandrepulsivedimensions into a general framework to overcome the weakness of traditional distance or similarity measures. We study the properties of the proposed class of scoring functions and develop efficient and scalable index structures that index the isolines of the function. We demonstrate various scenarios where the query finds application. Empirical evaluation demonstrates a performance gain of one to two orders of magnitude on querying time over existing state-of-the-art top-ktechniques. Further, a qualitative analysis is performed on a real dataset to highlight the potential of the proposed query in discovering hidden data characteristics.

Graphs are being increasingly used to model a wide range of scientific data. Such widespread usage of graphs has generated considerable interest in mining patterns from graph databases. While an array of techniques exists to mine frequent patterns, we still lack a scalable approach to mine statistically significant patterns, specifically patterns with low p-values, that occur at low frequencies. We propose a highly scalable technique, called GraphSig, to mine significant subgraphs from large graph databases. We convert each graph into a set of feature vectors where each vector represents a region within the graph. Domain knowledge is used to select a meaningful feature set. Prior probabilities of features are computed empirically to evaluate statistical significance of patterns in the feature space. Following analysis in the feature space, only a small portion of the exponential search space is accessed for further analysis. This enables the use of existing frequent subgraph mining techniques to mine significant patterns in a scalable manner even when they are infrequent. Extensive experiments are carried out on the proposed techniques, and empirical results demonstrate that GraphSig is effective and efficient for mining significant patterns. To further demonstrate the power of significant patterns, we develop a classifier using patterns mined by GraphSig. Experimental results show that the proposed classifier achieves superior performance, both in terms of quality and computation cost, over state-of-the-art classifiers.