Exact algorithms for finding well-connected 2-clubs in sparse real-world graphs: Theory and experiments

Christian Komusiewicz, André Nichterlein, Rolf Niedermeier and Marten Picker

European Journal of Operational Research, 2019, vol. 275, issue 3, 846-864

Abstract: Finding large “cliquish” subgraphs is a central topic in graph mining and community detection. A popular clique relaxation are 2-clubs: instead of asking for subgraphs of diameter one (these are cliques), one asks for subgraphs of diameter at most two (these are 2-clubs). A drawback of the 2-club model is that it produces star-like hub-and-spoke structures as maximum-cardinality solutions. Hence, we study 2-clubs with the additional constraint to be well-connected. More specifically, we investigate the algorithmic complexity for three variants of well-connected 2-clubs, all established in the literature: robust, hereditary, and “connected” 2-clubs. Finding these more cohesive 2-clubs is NP-hard; nevertheless, we develop an exact combinatorial algorithm, extensively using efficient data reduction rules. Besides several theoretical insights we provide a number of empirical results based on an engineered implementation of our exact algorithm. In particular, the algorithm significantly outperforms existing algorithms on almost all (sparse) real-world graphs we considered.

Keywords: Combinatorial optimization; Fixed-parameter tractability; Small-diameter subgraphs; Graph mining; Community detection (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:275:y:2019:i:3:p:846-864

DOI: 10.1016/j.ejor.2018.12.006

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