Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number

doi:10.1016/j.jda.2011.12.012

Journal of Discrete Algorithms

Volume 14, July 2012, Pages 207-213

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Abstract

The maximum independent set problem is known to be NP-hard for graphs in general, but is solvable in polynomial time for graphs in many special classes. It is also known that the problem is generally intractable from a parameterized point of view. A simple Ramsey argument implies the fixed-parameter tractability of the maximum independent set problem in classes of graphs of bounded clique number. Beyond this observation very little is known about the parameterized complexity of the problem in restricted graph families. In the present paper we develop fpt-algorithms for graphs in some classes extending graphs of bounded clique number.

Keywords

Independent set

Fixed-parameter tractability

Hereditary class of graphs

Modular decomposition

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^☆: This paper combines and extends results presented at the 21st International Workshop on Combinatorial Algorithms (IWOCAʼ10) and European Conference on Combinatorics, Graph Theory and Applications (EuroCombʼ09) and published as extended abstracts in Dabrowski et al. (2011) [7] and Lozin (2009) [16], respectively.

^☆☆: Research supported by the Centre for Discrete Mathematics and its Applications (DIMAP), EPSRC award EP/D063191/1.

¹: This author gratefully acknowledges support from EPSRC, grant EP/I01795X/1.

Journal of Discrete Algorithms

Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number☆,☆☆

Abstract

Keywords