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.
By: Francisco Barahona, Laszlo Ladanyi
Published in: RC22221 in 2001
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