Journal of Heuristics

, Volume 18, Issue 4, pp 525-547

First online:

Fast local search for the maximum independent set problem

  • Diogo V. AndradeAffiliated withGoogle Inc.
  • , Mauricio G. C. ResendeAffiliated withAT&T Labs Research Email author 
  • , Renato F. WerneckAffiliated withMicrosoft Research Silicon Valley

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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.


Maximum independent set Local search Iterated local search Algorithm engineering