Exact Algorithms for Dominating Clique Problems

Authors:
N. Bourgeois;F. Croce;B. Escoffier;V. Th. Paschos
Affiliations:
LAMSADE, CNRS and Université Paris-Dauphine, France;D.A.I., Politecnico di Torino, Italy;LAMSADE, CNRS and Université Paris-Dauphine, France;LAMSADE, CNRS and Université Paris-Dauphine, France
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

We handle in this paper three dominating clique problems, namely, the decision problem itself when one asks if there exists a dominating clique in a graph G and two optimization versions where one asks for a maximum- and a minimum-size dominating clique, if any. For the three problems we propose optimal algorithms with provably worst-case upper bounds improving existing ones by (D. Kratsch and M. Liedloff, An exact algorithm for the minimum dominating clique problem, Theoretical Computer Science 385(1-3), pp. 226---240, 2007). We then settle all the three problems in sparse and dense graphs also providing improved upper running time bounds.