Towards an Efficient Discovery of the Topological Representative Subgraphs

With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is still very high to be efficiently used in any further exploration. Feature selection for graph data is a way to reduce the high number of frequent subgraphs based on exact or approximate structural similarity. However, current structural similarity strategies are not efficient enough in many real-world applications, besides, the combinatorial nature of graphs makes it computationally very costly. In order to select a smaller yet structurally irredundant set of subgraphs, we propose a novel approach that mines the top-k topological representative subgraphs among the frequent ones. Our approach allows detecting hidden structural similarities that existing approaches are unable to detect such as the density or the diameter of the subgraph. In addition, it can be easily extended using any user defined structural or topological attributes depending on the sought properties. Empirical studies on real and synthetic graph datasets show that our approach is fast and scalable

What Makes a Good Plan? An Efficient Planning Approach to Control Diffusion Processes in Networks

In this paper, we analyze the quality of a large class of simple dynamic resource allocation (DRA) strategies which we name priority planning. Their aim is to control an undesired diffusion process by distributing resources to the contagious nodes of the network according to a predefined priority-order. In our analysis, we reduce the DRA problem to the linear arrangement of the nodes of the network. Under this perspective, we shed light on the role of a fundamental characteristic of this arrangement, the maximum cutwidth, for assessing the quality of any priority planning strategy. Our theoretical analysis validates the role of the maximum cutwidth by deriving bounds for the extinction time of the diffusion process. Finally, using the results of our analysis, we propose a novel and efficient DRA strategy, called Maximum Cutwidth Minimization, that outperforms other competing strategies in our simulations.Comment: 18 pages, 3 figure

Where Graph Topology Matters: The Robust Subgraph Problem

Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall vulnerability to external attacks or random failures. In this paper, we turn attention to local robustness and pose a novel problem in the lines of subgraph mining: given a large graph, how can we find its most robust local subgraph (RLS)? We define a robust subgraph as a subset of nodes with high communicability among them, and formulate the RLS-PROBLEM of finding a subgraph of given size with maximum robustness in the host graph. Our formulation is related to the recently proposed general framework for the densest subgraph problem, however differs from it substantially in that besides the number of edges in the subgraph, robustness also concerns with the placement of edges, i.e., the subgraph topology. We show that the RLS-PROBLEM is NP-hard and propose two heuristic algorithms based on top-down and bottom-up search strategies. Further, we present modifications of our algorithms to handle three practical variants of the RLS-PROBLEM. Experiments on synthetic and real-world graphs demonstrate that we find subgraphs with larger robustness than the densest subgraphs even at lower densities, suggesting that the existing approaches are not suitable for the new problem setting.Comment: 13 pages, 10 Figures, 3 Tables, to appear at SDM 2015 (9 pages only

Importance Sketching of Influence Dynamics in Billion-scale Networks

The blooming availability of traces for social, biological, and communication networks opens up unprecedented opportunities in analyzing diffusion processes in networks. However, the sheer sizes of the nowadays networks raise serious challenges in computational efficiency and scalability. In this paper, we propose a new hyper-graph sketching framework for inflence dynamics in networks. The central of our sketching framework, called SKIS, is an efficient importance sampling algorithm that returns only non-singular reverse cascades in the network. Comparing to previously developed sketches like RIS and SKIM, our sketch significantly enhances estimation quality while substantially reducing processing time and memory-footprint. Further, we present general strategies of using SKIS to enhance existing algorithms for influence estimation and influence maximization which are motivated by practical applications like viral marketing. Using SKIS, we design high-quality influence oracle for seed sets with average estimation error up to 10x times smaller than those using RIS and 6x times smaller than SKIM. In addition, our influence maximization using SKIS substantially improves the quality of solutions for greedy algorithms. It achieves up to 10x times speed-up and 4x memory reduction for the fastest RIS-based DSSA algorithm, while maintaining the same theoretical guarantees.Comment: 12 pages, to appear in ICDM 2017 as a regular pape

Mitigating Misinformation Spreading in Social Networks Via Edge Blocking

The wide adoption of social media platforms has brought about numerous benefits for communication and information sharing. However, it has also led to the rapid spread of misinformation, causing significant harm to individuals, communities, and society at large. Consequently, there has been a growing interest in devising efficient and effective strategies to contain the spread of misinformation. One popular countermeasure is blocking edges in the underlying network. We model the spread of misinformation using the classical Independent Cascade model and study the problem of minimizing the spread by blocking a given number of edges. We prove that this problem is computationally hard, but we propose an intuitive community-based algorithm, which aims to detect well-connected communities in the network and disconnect the inter-community edges. Our experiments on various real-world social networks demonstrate that the proposed algorithm significantly outperforms the prior methods, which mostly rely on centrality measures