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Semidefinite Programming Based Algorithms for the Sparsest Cut Problem
Published online by Cambridge University Press: 17 June 2011
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
$\frac{C}{W}$
and each heuristic produces a cut S with a ratio
$\frac{c_S}{w_S}$
, 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.
- Type
- Research Article
- Information
- Copyright
- © EDP Sciences, ROADEF, SMAI, 2011
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