SEMIDEFINITE PROGRAMMING BASED ALGORITHMS for the SPARSEST CUT PROBLEM

SEMIDEFINITE PROGRAMMING BASED ALGORITHMS for the SPARSEST CUT PROBLEM

Author Meira, Luis A. A. Autor UNIFESP Google Scholar
Miyazawa, Flavio K. Google Scholar
Institution Universidade Federal de São Paulo (UNIFESP)
Universidade Estadual de Campinas (UNICAMP)
Abstract In this paper we analyze a known relaxation for the Sparsest Cut problem based on positive semidefinite constraints, and we present a branch and bound algorithm and heuristics based on this relaxation. the relaxed formulation and the algorithms were tested on small and moderate sized instances. It leads to values very close to the optimum solution values. the exact algorithm could obtain solutions for small and moderate sized instances, and the best heuristics obtained optimum or near optimum solutions for all tested instances. the semidefinite relaxation gives a lower bound C/W and each heuristic produces a cut S with a ratio c(S)/omega(S) where either cs is at most a factor of C or omega(S) is at least a factor of W. We solved the semidefinite relaxation using a semi-infinite cut generation with a commercial linear programming package adapted to the sparsest cut problem. We showed that the proposed strategy leads to a better performance compared to the use of a. known semidefinite programming solver.
Keywords Semidefinite programming
Sparsest Cut
combinatorics
Language English
Sponsor Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Date 2011-04-01
Published in Rairo-operations Research. New York: Cambridge Univ Press, v. 45, n. 2, p. 75-100, 2011.
ISSN 0399-0559 (Sherpa/Romeo, impact factor)
Publisher Cambridge Univ Press
Extent 75-100
Origin http://dx.doi.org/10.1051/ro/2011104
Access rights Closed access
Type Article
Web of Science ID WOS:000296657000001
URI http://repositorio.unifesp.br/handle/11600/33612

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