Fractional packing of T-joins

Abstract

Given a graph with nonnegative capacities on its edges, it is well known that the capacity of a minimum T-cut is equal to the value of a maximum fractional packing of T-joins. The Padberg-Rao algorithm finds a minimum capacity T-cut, but it does not produce a T-join packing. We present a polynomial combinatorial algorithm for finding an optimal T-join packing.