Algorithms for dominating clique problems

Authors:
N. Bourgeois;F. Della Croce;B. Escoffier;V. Th. Paschos
Affiliations:
PSL Research University, Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, France;D.A.I., Politecnico di Torino, Italy;PSL Research University, Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, France;PSL Research University, Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, France and Institut Universitaire de France, France
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

We handle in this paper three dominating clique problems, namely, the decision problem to detect whether a graph has a dominating clique and two optimization versions asking to compute a maximum- and a minimum-size dominating clique of a graph G, if G has a dominating clique. For the three problems we propose exact moderately exponential algorithms with worst-case running time upper bounds improving those by Kratsch and Liedloff [D. Kratsch, M. Liedloff, An exact algorithm for the minimum dominating clique problem, Theoret. Comput. Sci. 385 (1-3) (2007) 226-240]. We then study the three problems in sparse and dense graphs also providing improved running time upper bounds. Finally, we propose some exponential time approximation algorithms for the optimization versions.