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

Abstract

An independent dominating set D of a graph G = (V,E) is a subset of vertices such that every vertex in V n D has at least one neighbor in D and D is an independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum independent dominating set in a graph is an NP-hard problem. Whereas it is hard to cope with this problem using parameterized and approximation algorithms, there is a simple exact O(1,4423 n)-time algorithm solving the problem by enumerating all maximal independent sets. In this paper we improve the latter result, providing the first non-trivial algorithm computing a minimum independent dominating set of a graph in time O(1,3569 n). Furthermore, we give a lower bound of σ(1,3247 n) on the worst-case running time of this algorithm, showing that the running time analysis is almost tight. © 2012 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.