Fast algorithms for min independent dominating set

Authors:
Nicolas Bourgeois;Bruno Escoffier;Vangelis Th. Paschos
Affiliations:
LAMSADE, CNRS and Université Paris-Dauphine, Paris, France;LAMSADE, CNRS and Université Paris-Dauphine, Paris, France;LAMSADE, CNRS and Université Paris-Dauphine, Paris, France
Venue:
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Year:
2010

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Abstract

We first devise a branching algorithm that computes a minimum independent dominating set with running time O*(20.424n) and polynomial space. This improves the O*(20.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then study approximation of the problem by moderately exponential algorithms and show that it can be approximated within ratio 1+ε, for any ε0, in a time smaller than the one of exact computation and exponentially decreasing with ε. We also propose approximation algorithms with better running times for ratios greater than 3.