%0 Journal Article %T A Geometrical Explanation to the Optimality Concept of Minimum Cost Flows %J Scientia Iranica %I Sharif University of Technology %Z 1026-3098 %A Ghiyasvand, Mehdi %D 2016 %\ 12/01/2016 %V 23 %N 6 %P 3063-3071 %! A Geometrical Explanation to the Optimality Concept of Minimum Cost Flows %K Operations research %K Network Flows Optimization %K The Minimum Cost Flow Proble %R 10.24200/sci.2016.4012 %X Shigeno et al.'s algorithm(2000) is a scaling method to solveĀ  the minimum cost flow problem. In each phase, they applied the most positive cut canceling idea. In this paper, we present a new approach to solve the problem, which uses the scaling method of Shigeno et al.(2000), but, in each phase, we apply the out-of-kilter idea instead of the most positive cut canceling idea. Our algorithm is inspired by Ghiyasvand(2012). The algorithmĀ  gives a geometrical explanation to the optimality concept. For a network with $n$ nodes and $m$ arcs, the algorithm performs $O(log (nU))$ phases and runs in $O(m(m+nlog n)log (nU))$ time (where $U$ is the largest absolute arc bound ), which is $O(m(m+nlog n)log n)$ under the similarity assumption. This time is the running time of the algorithms by Orlincite{O} and Vygencite{V} which are the best strongly polynomial-time algorithms to solve this problem. %U https://scientiairanica.sharif.edu/article_4012_4b9e7302524d0960c3ecc694ae299f55.pdf