A d/2 Approximation for Maximum Weight Independent Set in d-Claw Free Graphs

Abstract

A graph is d-claw free if no node has d distinct independent neighbors. In the most usual applications, the nodes of this graph form a family of sets with fewer than d elements, and the edges indicate overlapping pairs of sets. Consequently, an independent set in the graph is a packing in our family of sets. In this paper we consider the following problem. Given is a d-claw free graph G = (V, E, w) where w : V \textrightarrow IR+. We describe an algorithm with running time polynomial in \textbarV\textbard that finds an independent set A such that w(A*)/w(A)