FPT algorithms for finding near-cliques in c-closed graphs

Behera, Balaram, Husić, Edin ORCID: 0000-0002-6708-5112, Jain, Shweta, Roughgarden, Tim and Seshadhri, C. (2022) FPT algorithms for finding near-cliques in c-closed graphs. In: Braverman, Mark, (ed.) 13th Innovations in Theoretical Computer Science Conference, ITCS 2022. Leibniz International Proceedings in Informatics, LIPIcs. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 17:1 - 17:24. ISBN 9783959772174

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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.

Item Type:	Book Section
Official URL:	https://drops.dagstuhl.de/opus/institut_lipics.php
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	17 Feb 2022 17:48
Last Modified:	11 Dec 2024 18:05
URI:	http://eprints.lse.ac.uk/id/eprint/113778

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