Decremental clique problem

Authors:
Fabrizio Grandoni;Giuseppe F. Italiano
Affiliations:
Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, Roma, Italy;Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, Roma, Italy
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

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Abstract

The clique problem consists in determining whether an undirected graph G of order n contains a clique of order ℓ. In this paper we are concerned with the decremental version of clique problem, where the property of containing an ℓ-clique is dynamically checked during deletions of nodes. We provide an improved dynamic algorithm for this problem for every fixed value of ℓ ≥ 3. Our algorithm naturally applies to filtering for the constraint satisfaction problem. In particular, we show how to speed up the filtering based on an important local consistency property: the inverse consistency.