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 \ 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 \Omega(1.3247^n) on the worst-case running time of this algorithm, showing that the running time analysis is almost tight.
Cite
@article{arxiv.1009.1381,
title = {A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set},
author = {Serge Gaspers and Mathieu Liedloff},
journal= {arXiv preprint arXiv:1009.1381},
year = {2010}
}
Comments
Full version. A preliminary version appeared in the proceedings of WG 2006