Segmentation Meets Densest Subgraph Discovery
Knowledge and Information Systems https://doi.org/10.1007/s10115-019-01403-9 REGULAR PAPER Finding events in temporal networks: segmentation meets densest subgraph discovery Polina Rozenshtein1,7 · Francesco Bonchi2,3 · Aristides Gionis1 · Mauro Sozio4 · Nikolaj Tatti5,6 Received: 5 January 2019 / Revised: 4 September 2019 / Accepted: 13 September 2019 © The Author(s) 2019 Abstract In this paper, we study the problem of discovering a timeline of events in a temporal net- work. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the net- work lifetime. A naïve solution to our optimization problem has polynomial but prohibitively high running time. We adapt existing recent work on dynamic densest subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard; however, we show that on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extend this greedy approach for temporal networks, but we lose the approximation guarantee in the process. Finally, we demonstrate empirically that our algorithms recover solutions with good quality. Keywords Densest subgraph · Segmentation · Dynamic programming · Approximate algorithm B Polina Rozenshtein polina.rozenshtein@aalto.fi 1 Department of Computer Science, Aalto University, Espoo, Finland 2 ISI Foundation, Turin, Italy 3 Eurecat, Barcelona, Spain 4 Telecom ParisTech University, Paris, France 5 F-Secure Corporation, Helsinki, Finland 6 University of Helsinki, Helsinki, Finland 7 Nordea Data Science Lab, Helsinki, Finland 123 P.
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