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2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM) (2016)
San Francisco, CA, USA
Aug. 18, 2016 to Aug. 21, 2016
ISBN: 978-1-5090-2847-4
pp: 337-344
Anne-Sophie Himmel , Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany
Hendrik Molter , Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany
Rolf Niedermeier , Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany
Manuel Sorge , Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany
ABSTRACT
Dynamics of interactions play an increasingly important role in the analysis of complex networks. A modeling framework to capture this are temporal graphs. We focus on enumerating Δ-cliques, an extension of the concept of cliques to temporal graphs: for a given time period Δ, a Δ-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 Δ time steps within the time interval. Viard, Latapy, and Magnien [ASONAM 2015] proposed a greedy algorithm for enumerating all maximal Δ-cliques in temporal graphs. In contrast to this approach, we adapt to the temporal setting the Bron-Kerbosch algorithm — an efficient, recursive backtracking algorithm which enumerates all maximal cliques in static graphs. We obtain encouraging results both in theory (concerning worst-case time analysis based on the parameter “Δ-slice degeneracy” of the underlying graph) as well as in practice with experiments on real-world data. The latter culminates in a significant improvement for most interesting Δ-values concerning running time in comparison with the algorithm of Viard, Latapy, and Magnien (typically two orders of magnitude).
INDEX TERMS
Algorithm design and analysis, Standards, Heuristic algorithms, Social network services, Adaptation models, Upper bound, Complex networks
CITATION

A. Himmel, H. Molter, R. Niedermeier and M. Sorge, "Enumerating maximal cliques in temporal graphs," 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), San Francisco, CA, USA, 2016, pp. 337-344.
doi:10.1109/ASONAM.2016.7752255
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