Journal article
Maximum stable set formulations and heuristics based on continuous optimization
Mathematical programming, Vol.94(1), pp.137-166
12/01/2002
DOI: 10.1007/s10107-002-0356-4
Abstract
The stability number α(G) for a given graph G is the size of a maximum stable set in G. The Lovász theta number provides an upper bound on α(G) and can be computed in polynomial time as the optimal value of the Lovász semidefinite program. In this paper, we show that restricting the matrix variable in the Lovász semidefinite program to be rank-one and rank-two, respectively, yields a pair of continuous, nonlinear optimization problems each having the global optimal value α(G). We propose heuristics for obtaining large stable sets in G based on these new formulations and present computational results indicating the effectiveness of the heuristics.
Details
- Title: Subtitle
- Maximum stable set formulations and heuristics based on continuous optimization
- Creators
- Samuel Burer - University of IowaRenato D. C Monteiro - Georgia Institute of TechnologyYIN Zhang - Rice University
- Resource Type
- Journal article
- Publication Details
- Mathematical programming, Vol.94(1), pp.137-166
- Publisher
- Springer
- DOI
- 10.1007/s10107-002-0356-4
- ISSN
- 0025-5610
- eISSN
- 1436-4646
- Language
- English
- Date published
- 12/01/2002
- Academic Unit
- Business Analytics
- Record Identifier
- 9984380525302771
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