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

Francisco Barahona (barahonus.ibm.com)
Lazslo Ladanyi (ladanyius.ibm.com)

Abstract: We present a Branch-and-Cut algorithm where the Volume Algorithm is applied to the linear programming relaxations arising at each node of the search tree. This means we use fast approximate solutions to these linear programs instead of exact but slower solutions given by the traditionally used dual simplex method. Our claim is that such a Branch-and-Cut code should work well for problems whose linear programming relaxation is well suited to be solved with the Volume Algorithm. We present computational results with the Max-Cut and Steiner Tree 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.

Keywords: volume algorithm, branch-and-cut, Steiner trees in graphs, max-cut

Category 1: Combinatorial Optimization (Branch and Cut Algorithms )

Citation: IBM report RC22221, October 2001

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Entry Submitted: 12/26/2001
Entry Accepted: 12/27/2001
Entry Last Modified: 06/21/2004

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