A Polynomial Time Algorithm for the Minimum Cost Flow Problem

Abstract

An efficient polynomial time algorithm for
solving minimum cost flow problems has been proposed
in this paper. This algorithm is basically based on
successive divisions of capacities by multiples of two,
and it solves the minimum cost flow problem as a
sequence of O(n2 ) shortest path problems on residual
networks with n nodes and runs in O(n2m r ) time,
where m is the number of arcs and r is the smallest
integer greater than or equal to log B , and B is the
largest arc capacity of the network. A numerical
example is illustrated using the proposed algorithm.