Finding Top-k Shortest Path Distance Changes in an Evolutionary Network

Gupta, Manish; Aggarwal, Charų C.

doi:10.1007/978-3-642-22922-0_9

Cited by 11 publications

(3 citation statements)

References 26 publications

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“…Surprisingly, a simple variant to check the existence of a temporal path with waiting time constraints was shown to be NP-complete by Casteigts et al [12], more strongly, they proved that the problem is W[1]-hard. A known variant of the temporal-path problem is finding top-k shortest paths, which not only asks us to find a shortest path, but also the next k − 1 shortest paths -which may be longer than the shortest path [26]. Here by shortest path we mean that the total elapsed time of the temporal path is minimized.…”

Section: Related Workmentioning

confidence: 99%

Pattern detection in large temporal graphs using algebraic fingerprints

Thejaswi¹,

Gionis²

2020

Proceedings of the 2020 SIAM International Conference on Data Mining

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In this paper we study a family of pattern-detection problems in vertex-colored temporal graphs. In particular, given a vertex-colored temporal graph and a multi-set of colors as a query, we search for temporal paths in the graph that contain the colors specified in the query. These types of problems have several interesting applications, for example, recommending tours for tourists, or searching for abnormal behavior in a network of financial transactions.For the family of pattern-detection problems we define, we establish complexity results and design an algebraic-algorithmic framework based on constrained multilinear sieving. We demonstrate that our solution can scale to massive graphs with up to hundred million edges, despite the problems being NP-hard. Our implementation, which is publicly available, exhibits practical edge-linear scalability and highly optimized. For example, in a real-world graph dataset with more than six million edges and a multi-set query with ten colors, we can extract an optimal solution in less than eight minutes on a haswell desktop with four cores.

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Section: Related Workmentioning

confidence: 99%

Pattern detection in large temporal graphs using algebraic fingerprints

Thejaswi¹,

Gionis²

2020

Proceedings of the 2020 SIAM International Conference on Data Mining

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“…Path problems in temporal graphs are well studied [19,38,39]. A number of problem variants that seek to find a path that minimizes different objectives, such as path length, arrival time, or duration, as well as finding top-𝑘 shortest temporal paths are solvable in polynomial time [19,20,38,39,41]. In recent years, there has been emphasis on temporal-path problems due to their applicability in various fields [3,12,30,36].…”

Section: Related Workmentioning

confidence: 99%

Restless reachability problems in temporal graphs

Thejaswi¹,

Lauri²,

Gionis³

2020

Preprint

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We study a family of temporal reachability problems under waiting-time restrictions. In particular, given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via a time-respecting path, and such that the difference in timestamps between consecutive edges is at most a resting time. This kind of problems have several interesting applications in understanding the spread of a disease in a network, tracing contacts in epidemic outbreaks, and finding signaling pathways in the brain network.We present an algebraic algorithm based on constrained multilinear sieving for solving the restless reachability problems we propose. With an open-source implementation we demonstrate that the algorithm can scale to large temporal graphs with tens of millions of edges, despite the problem being NP-hard. The implementation is efficiently engineered and highly optimized. For instance, we can solve the restless reachability problem by restricting the path length to 9 in a real-world graph dataset with over 36 million directed edges in less than one hour on a 4-core Haswell desktop.

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“…In contrast, more recent tools go farther in the adaptation of these static methods to the analysis of dynamic networks and better describe or detect the changes caused by temporal evolution. For instance, Gupta et al (2011) describe a method allowing to detect the most significant changes in the distance between nodes, assuming such changes correspond to important events in the evolution of the graph.…”

Section: Related Workmentioning

confidence: 99%

Exploring the evolution of node neighborhoods in Dynamic Networks

Orman

Labatut

Naskalı

2017

Physica A: Statistical Mechanics and its Applications

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Dynamic Networks are a popular way of modeling and studying the behavior of evolving systems. However, their analysis constitutes a relatively recent subfield of Network Science, and the number of available tools is consequently much smaller than for static networks. In this work, we propose a method specifically designed to take advantage of the longitudinal nature of dynamic networks. It characterizes each individual node by studying the evolution of its direct neighborhood, based on the assumption that the way this neighborhood changes reflects the role and position of the node in the whole network. For this purpose, we define the concept of neighborhood event, which corresponds to the various transformations such groups of nodes can undergo, and describe an algorithm for detecting such events. We demonstrate the interest of our method on three real-world networks: DBLP, LastFM and Enron. We apply frequent pattern mining to extract meaningful information from temporal sequences of neighborhood events. This results in the identification of behavioral trends emerging in the whole network, as well as the individual characterization of specific nodes. We also perform a cluster analysis, which reveals that, in all three networks, one can distinguish two types of nodes exhibiting different behaviors: a very small group of active nodes, whose neighborhood undergo diverse and frequent events, and a very large group of stable nodes. density, network diameter (Leskovec et al. 2005a). Second, mesoscopic methods consider the network at an intermediary level, generally that of the community structure, e.g. modularity measure (Kashtan and Alon 2005), size of the communities (Backstrom et al. 2006). Finally, microscopic methods focus on individual nodes and possibly their direct neighborhood, e.g. clustering coefficient (Clauset and Eagle 2007).By definition, methods specifically designed to handle a dynamic network are more likely to take advantage of the specificity of such data. Regarding the granularity, if macroscopic and mesoscopic methods are widespread in the literature, it is not the case for microscopic methods. Yet, the benefits of such approaches are numerous: by allowing the tracking of finer evolution processes, they complement macroscopic and/or mesoscopic results. They help identifying behavioral trends among the network nodes, and consequently outliers. These results can facilitate the description and understanding of processes observed at a higher level, and can be useful to define models of the studied system, especially agent-based ones.In this work, we propose a method specifically designed to study dynamic slowly evolving networks, at the microscopic level. We characterize a node by the evolution of its neighborhood. More precisely, we detect specific events occurring among the groups of nodes constituting this neighborhood, between each pair of consecutive time slices, which we call neighborhood evolution events. This method constitutes our main contribution. To the best of our knowledge, it is the fir...

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Finding Top-k Shortest Path Distance Changes in an Evolutionary Network

Cited by 11 publications

References 26 publications

Pattern detection in large temporal graphs using algebraic fingerprints

Pattern detection in large temporal graphs using algebraic fingerprints

Restless reachability problems in temporal graphs

Exploring the evolution of node neighborhoods in Dynamic Networks

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