Computing Weighted Maximal Flows in Polymatroidal Networks

For the polymatroidal network, which has set-constraints on arcs, solution procedures to get the weighted maximal flows are investigated. These procedures are composed of the transformation of the polymatroidal network flow problem into a polymatroid intersection problem and a polymatroid intersection algorithm. A greedy polymatroid intersection algorithm is presented, and an example problem is solved. The greedy polymatroid intersection algorithm is a variation of Hassin's. According to these procedures, there is no need to convert the primal problem concerned into dual one. This differs from the procedures of Hassin, in which the dual restricted problem is used.