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Computer Science > Data Structures and Algorithms

arXiv:1605.03871 (cs)
[Submitted on 12 May 2016 (v1), last revised 2 May 2017 (this version, v2)]

Title:Adapting the Bron-Kerbosch Algorithm for Enumerating Maximal Cliques in Temporal Graphs

Authors:Anne-Sophie Himmel, Hendrik Molter, Rolf Niedermeier, Manuel Sorge
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Abstract:Dynamics of interactions play an increasingly important role in the analysis of complex networks. A modeling framework to capture this are temporal graphs which consist of a set of vertices (entities in the network) and a set of time-stamped binary interactions between the vertices. We focus on enumerating delta-cliques, an extension of the concept of cliques to temporal graphs: for a given time period delta, a delta-clique in a temporal graph is a set of vertices and a time interval such that all vertices interact with each other at least after every delta time steps within the time interval. Viard, Latapy, and Magnien [ASONAM 2015, TCS 2016] proposed a greedy algorithm for enumerating all maximal delta-cliques in temporal graphs. In contrast to this approach, we adapt the Bron-Kerbosch algorithm - an efficient, recursive backtracking algorithm which enumerates all maximal cliques in static graphs - to the temporal setting. We obtain encouraging results both in theory (concerning worst-case running time analysis based on the parameter "delta-slice degeneracy" of the underlying graph) as well as in practice with experiments on real-world data. The latter culminates in an improvement for most interesting delte-values concerning running time in comparison with the algorithm of Viard, Latapy, and Magnien.
Subjects: Data Structures and Algorithms (cs.DS); Computational Complexity (cs.CC); Social and Information Networks (cs.SI)
Cite as: arXiv:1605.03871 [cs.DS]
  (or arXiv:1605.03871v2 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.1605.03871

Submission history

From: Hendrik Molter [view email]
[v1] Thu, 12 May 2016 15:59:48 UTC (32 KB)
[v2] Tue, 2 May 2017 16:02:55 UTC (206 KB)
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Hendrik Molter
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