Improved approximations of independent sets in bounded-degree graphs via subgraph removal

Abstract

Finding maximum independent sets in graphs with bounded maximum degree Δ is a well-studied NP-complete problem. We introduce an algorithm schema for improving the approximation of algorithms for this problem, which is based on preprocessing the input by removing cliques.We give an implementation of a theorem on the independence number of clique-free graphs, and use it to obtain an O(Δ/log log Δ) performance ratio with our schema. This is the first o(Δ) ratio for the independent set problem. We also obtain an efficient method with a Δ/6(1 + o(1)) performance ratio, improving on the best performance ratio known for intermediate values of Δ.