Abstract
Given a capacitated network with the entrance-vertex set V_1 and the exit-vertex set V_2 on which polymatroids are defined, an independent flow is a flow in the network such that a vector corresponding to the supplies in V_1 and a vector corresponding to the demands in V_2 are, respectively, independent vectors of the polymatroids on V_1 and V_2 ・ The independent-flow problems considered in the present paper are the following two: (1) to find a maximum independent flow; and (2) to find an optimal independent flow, i,e,, a maximum independent flow of the minimum cost when a cost is given to each arc, We present several theorems which algorithmically characterize optimal independent flows and we propose algorithms for solving the independent-flow problems based on the theorems.
