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• W3217648011 abstract "Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective backtracking-based heuristics for these problems have emerged from recent empirical work in social network analysis. Given the NP-hardness of variants of clique counting, these results raise a challenge for beyond worst-case analysis of these problems. Inspired by the triadic closure of real-world graphs, Fox et al. (SICOMP 2020) introduced the notion of $c$-closed graphs and proved that maximal clique enumeration is fixed-parameter tractable with respect to $c$. In practice, due to noise in data, one wishes to actually discover near-cliques, which can be characterized as cliques with a sparse subgraph removed. In this work, we prove that many different kinds of maximal near-cliques can be enumerated in polynomial time (and FPT in $c$) for $c$-closed graphs. We study various established notions of such substructures, including $k$-plexes, complements of bounded-degeneracy and bounded-treewidth graphs. Interestingly, our algorithms follow relatively simple backtracking procedures, analogous to what is done in practice. Our results underscore the significance of the $c$-closed graph class for theoretical understanding of social network analysis." @default.
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• W3217648011 date "2020-07-19" @default.
• W3217648011 modified "2023-10-14" @default.
• W3217648011 title "FPT Algorithms for Finding Near-Cliques in $c$-Closed Graphs" @default.
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• W3217648011 doi "https://doi.org/10.48550/arxiv.2007.09768" @default.
• W3217648011 hasPublicationYear "2020" @default.
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