Improved approximations of independent sets in bounded-degree graphs via subgraph removal
Magnús M. Halldórsson, Jaikumar Radhakrishnan · 1994
Finding maximum independent sets in graphs with bounded maximum degree 1 is a well-studied N P-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(1 = log log 1) performance ratio with our schema. This is the first o(1) ratio for the independent set problem. We also obtain an efficient method with a 1=6(1 + o(1)) performance ratio, improving on the best performance ratio known for intermediate values of 1.