Fast local search for the maximum independent set problem

Authors:
Diogo V. Andrade;Mauricio G. C. Resende;Renato F. Werneck
Affiliations:
Google Inc., New York, NY;AT&T Labs Research, Florham Park, NJ;Microsoft Research Silicon Valley, Mtn. View, CA
Venue:
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Year:
2008

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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 present a fast local search routine for this problem. Our algorithm can determine in linear time whether a maximal solution can be improved by replacing a single vertex with two others. We also show that an incremental version of this method can be useful within more elaborate heuristics. We test our algorithms on instances from the literature as well as on new ones proposed in this paper.