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Branch and Cut based on the volume algorithm: Steiner trees in graphs and Max-cut

Published online by Cambridge University Press:  01 July 2006

Francisco Barahona  and
László Ladányi
Francisco Barahona
Affiliation:
IBM T. J. Watson research Center, Yorktown Heights, NY 10589, USA; [email protected]; [email protected]
László Ladányi
Affiliation:
IBM T. J. Watson research Center, Yorktown Heights, NY 10589, USA; [email protected]; [email protected]
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Abstract

We present a Branch-and-Cut algorithm where the volume algorithm is applied instead of the traditionally used dual simplex algorithm to the linear programming relaxations in the root node of the search tree. This means that we use fast approximate solutions to these linear programs instead of exact but slower solutions. We present computational results with the Steiner tree and Max-Cut problems. We show evidence that one can solve these problems much faster with the volume algorithm based Branch-and-Cut code than with a dual simplex based one. We discuss when the volume based approach might be more efficient than the simplex based approach.

Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 1 , January 2006 , pp. 53 - 73
Copyright
© EDP Sciences, 2006

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