A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set

Serge Gaspers (1) , Mathieu Liedloff (2)

1 Institute of Information Systems
2 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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.

Domaines: Algorithme et structure de données [cs.DS]

Serge Gaspers, Mathieu Liedloff. A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set. Discrete Mathematics and Theoretical Computer Science, 2012, Vol. 14 no. 1 (1), pp.29-42. ⟨10.46298/dmtcs.563⟩. ⟨hal-00942912⟩