Abstract
This paper deals with a minimum cost flow problem. We propose a polynomial time algorithm for the problem. The algorithm is based on an interior point algorithm for a general linear programming problem. Using some features of the minimum cost flow problem, we decrease the running time. We show that the algorithm requires at most O(|El|^<0.5>log(|V|M)) iterations, O(|V|^3) arithmetic operations in each iteration, and O(|V|^3|E|^<0.5>log(|V|M)) arithmetic operations in total. Here |V|, |E| and M denote the number of nodes, that of arcs, and the maximum absolute value of input data, respectively.
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