Maximum independent set in graphs of average degree at most three in O(1.08537n)

Authors:
Nicolas Bourgeois;Bruno Escoffier;Vangelis Th. Paschos;Johan M M. van Rooij
Affiliations:
LAMSADE, CNRS FRE 3234 and Université Paris-Dauphine, France;LAMSADE, CNRS FRE 3234 and Université Paris-Dauphine, France;LAMSADE, CNRS FRE 3234 and Université Paris-Dauphine, France;Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands
Venue:
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Year:
2010

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Abstract

We show that Maximum Independent Set on connected graphs of average degree at most three can be solved in ${\mathcal O}(1.08537^n)$ time and linear space This improves previous results on graphs of maximum degree three, as our connectivity requirement only functions to ensure that each connected component has average degree at most three. We link this result to exact algorithms of Maximum Independent Set on general graphs Also, we obtain a faster parameterised algorithm for Vertex Cover restricted to graphs of maximum degree three running in time ${\mathcal O}^*(1.1781^k)$.