Gaspers, Serge and Liedloff, Mathieu - A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set

dmtcs:563 - Discrete Mathematics & Theoretical Computer Science, February 7, 2012, Vol. 14 no. 1
A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set

Authors: Gaspers, Serge and Liedloff, Mathieu

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.


Source : oai:HAL:hal-00942912v1
Volume: Vol. 14 no. 1
Section: Graph and Algorithms
Published on: February 7, 2012
Submitted on: September 7, 2010
Keywords: [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]


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