Fast local search for the maximum independent set problem

D.V. Andrade,  M. G. C. Resende, and R.F. Werneck 

J. of Heuristics, vol. 18, pp. 525-547, 2012.


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(mD) time (where D 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.

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