Fast local search for the maximum independent set problem

  • Authors:

  • Diogo V. Andrade;Mauricio G. Resende;Renato F. Werneck

  • Affiliations:

  • Google Inc., New York, USA 10011;AT&T Labs Research, Florham Park, USA 07932;Microsoft Research Silicon Valley, Mtn. View, USA 94043

  • Venue:
  • Journal of Heuristics
  • Year:
  • 2012

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Abstract

Given a graph G=(V,E), the independent set problem is that of finding a maximum-cardinality subset S of V such that no two vertices in S are adjacent. We introduce two fast local search routines for this problem. The first can determine in linear time whether a maximal solution can be improved by replacing a single vertex with two others. The second routine can determine in O(mΔ) time (where Δ is the highest degree in the graph) whether there are two solution vertices than can be replaced by a set of three. We also present a more elaborate heuristic that successfully applies local search to find near-optimum solutions to a wide variety of instances. We test our algorithms on instances from the literature as well as on new ones proposed in this paper.