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dc.contributor.authorYıldırım, E. A.en_US
dc.contributor.authorFan-Orzechowski, X.en_US
dc.date.accessioned2016-02-08T10:20:03Z
dc.date.available2016-02-08T10:20:03Z
dc.date.issued2006en_US
dc.identifier.issn0926-6003
dc.identifier.urihttp://hdl.handle.net/11693/23840
dc.description.abstractWe study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lovász's theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its induced subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a perfect graph using the theta function. Our algorithm iteratively transforms an approximate solution of the semidefinite formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex that belongs to a maximum stable set. The subgraph induced by that vertex and its neighbors is removed and the same procedure is repeated on successively smaller graphs. We establish that solving the theta problem up to an adaptively chosen, fairly rough accuracy suffices in order for the algorithm to work properly. Furthermore, our algorithm successfully employs a warm-start strategy to recompute the theta function on smaller subgraphs. Computational results demonstrate that our algorithm can efficiently extract maximum stable sets in comparable time it takes to solve the theta problem on the original graph to optimality.en_US
dc.language.isoEnglishen_US
dc.source.titleComputational Optimization and Applicationsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s10589-005-3060-5en_US
dc.subjectMaximum stable setsen_US
dc.subjectLovasz’s theta functionen_US
dc.subjectSemidefinite programmingen_US
dc.subjectPerfect graphsen_US
dc.titleOn extracting maximum stable sets in perfect graphs using Lovász's theta functionen_US
dc.typeArticleen_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.citation.spage229en_US
dc.citation.epage247en_US
dc.citation.volumeNumber33en_US
dc.citation.issueNumber2-3en_US
dc.identifier.doi10.1007/s10589-005-3060-5en_US
dc.publisherSpringeren_US
dc.identifier.eissn1573-2894


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