Improved Approximations of Independent Sets in Bounded-Degree Graphs

Abstract. Finding maximum independent sets in graphs with bounded maximum degree 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 cliquefree graphs, and use it to obtain an O(/ log log ) performance ratio with our schema. This is the first o() ratio for the independent set problem. We also obtain an efficient method with a /6(1 + o(1)) performance ratio, improving on the best performance ratio known for intermediate values of . CR Classification: F.2.2, G.2.2 Key words: analysis of algorithms, approximation algorithms, independent sets

• Type: Conference
• Year: 1994
• Where: SWAT
• Authors: Magnús M. Halldórsson, Jaikumar Radhakrishnan
• Keywords: Algorithms, Independent Sets, Performance Ratio, SWAT 1994, Well-studied Np-complete Problem