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DOI: 10.4230/LIPIcs.ITCS.2022.17

FPT Algorithms for Finding Near-Cliques in c-Closed Graphs

Authors: Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, and C. Seshadhri

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

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.

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Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, and C. Seshadhri. FPT Algorithms for Finding Near-Cliques in c-Closed Graphs. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 17:1-17:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{behera_et_al:LIPIcs.ITCS.2022.17,
  author =	{Behera, Balaram and Husi\'{c}, Edin and Jain, Shweta and Roughgarden, Tim and Seshadhri, C.},
  title =	{{FPT Algorithms for Finding Near-Cliques in c-Closed Graphs}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{17:1--17:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.17},
  URN =		{urn:nbn:de:0030-drops-156130},
  doi =		{10.4230/LIPIcs.ITCS.2022.17},
  annote =	{Keywords: c-closed graph, dense subgraphs, FPT algorithm, enumeration algorithm, k-plex, Moon-Moser theorem}
}

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1 Search Results for "Jain, Shweta"

FPT Algorithms for Finding Near-Cliques in c-Closed Graphs

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