Volume 45, Number 2, April-June 2011
|Page(s)||75 - 100|
|Published online||17 June 2011|
Semidefinite Programming Based Algorithms for the Sparsest Cut Problem
Federal University of Sao Paulo, Rua botucatu 740 Edif Octavio de Carvalho, 04023-900
Sao Paulo, Brazil. email@example.com
2 University of Campinas, Brazil. firstname.lastname@example.org
Accepted: 22 April 2011
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 and each heuristic produces a cut S with a ratio , where either cS is at most a factor of C or wS 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.
Mathematics Subject Classification: 90C22 / 90C57 / 68Q87
Key words: Semidefinite programming / Sparsest Cut / combinatorics
© EDP Sciences, ROADEF, SMAI, 2011
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