Fast local search for the maximum independent set problem
 Diogo V. Andrade,
 Mauricio G. C. Resende,
 Renato F. Werneck
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Given a graph G=(V,E), the independent set problem is that of finding a maximumcardinality 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 nearoptimum 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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 Title
 Fast local search for the maximum independent set problem
 Journal

Journal of Heuristics
Volume 18, Issue 4 , pp 525547
 Cover Date
 20120801
 DOI
 10.1007/s1073201291964
 Print ISSN
 13811231
 Online ISSN
 15729397
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Maximum independent set
 Local search
 Iterated local search
 Algorithm engineering
 Industry Sectors
 Authors

 Diogo V. Andrade ^{(1)}
 Mauricio G. C. Resende ^{(2)}
 Renato F. Werneck ^{(3)}
 Author Affiliations

 1. Google Inc., 76 Ninth Avenue, New York, NY, 10011, USA
 2. AT&T Labs Research, 180 Park Ave, Florham Park, NJ, 07932, USA
 3. Microsoft Research Silicon Valley, 1065 La Avenida, Mtn. View, CA, 94043, USA