# 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.

Published

2018-05-11

How to Cite

TLAS, M..
A Polynomial Time Algorithm for the Minimum Cost Flow Problem.

**GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR)**, [S.l.], v. 2, n. 1, may 2018. ISSN 2251-3396. Available at: <http://dl6.globalstf.org/index.php/jmsor/article/view/1538>. Date accessed: 25 june 2019.