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.
IBM report RC22221, October 2001