Fast local search for the maximum independent set problem

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...

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Bibliographic Details
Published in:Journal of heuristics Vol. 18; no. 4; pp. 525 - 547
Main Authors: Andrade, Diogo V., Resende, Mauricio G. C., Werneck, Renato F.
Format: Journal Article
Language:English
Published: Boston Springer US 01.08.2012
Springer Science + Business Media
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Engineering
Heuristic
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Studies
Maximum independent set
Local search
Algorithm engineering
Iterated local search
ISSN:1381-1231, 1572-9397
Online Access:Get full text
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Summary: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 ( m Δ) 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.
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ISSN:1381-1231
1572-9397
DOI:10.1007/s10732-012-9196-4