Strongly polynomial algorithm for two special minimum concave cost network flow problems

Abstract

We consider two special cases of the Minimum Concave Cost Network Flow Problem (MCCNFP);the single source uncapacitated MCCNFP where all arc costs, except two, are linear and the uncapacitated MCCNFP with 2 sources and 1 nonlinear arc cost. Due to their specific structure these problems can he solved by efficient strongly polynomial time algorithms. More specifically, the algorithms developed have running times polynomial in the number of nodes and arcs and the number of sinks