A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs

Authors:
Serge Gaspers;Mathieu Liedloff
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;Laboratoire d'Informatique Théorique et Appliquée, Université Paul, Verlaine – Metz, Metz, France
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

Citing 9
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Abstract

A dominating set of a graph G = (V,E) is a subset of vertices such that every vertex in has at least one neighbour in . Moreover if is an independent set, i.e. no vertices in are pairwise adjacent, then is said to be an independent dominating set. Finding a minimum independent dominating set in a graph is an NP-hard problem. We give an algorithm computing a minimum independent dominating set of a graph on n vertices in time O(1.3575n). Furthermore, we show that Ω(1.3247n) is a lower bound on the worst-case running time of this algorithm.