Parameterized Algorithms for the Independent Set Problem in Some Hereditary Graph Classes

Abstract

The maximum independent set problem is NP-complete for graphs in general, but becomes solvable in polynomial time when restricted to graphs in many special classes. The problem is also intractable from a parameterized point of view. However, very little is known about parameterized complexity of the problem in restricted graph classes. In the present paper, we analyse two techniques that have previously been used to solve the problem in polynomial time for graphs in particular classes and apply these techniques to develop fpt-algorithms for graphs in some classes where the problem remains NP-complete.