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A capacity-rounding algorithm for the minimum-cost circulation problem: A dual framework of the Tardos algorithm

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Abstract

Recently, É. Tardos gave a strongly polynomial algorithm for the minimum-cost circulation problem and solved the open problem posed in 1972 by J. Edmonds and R.M. Karp. Her algorithm runs in O(m 2 T(m, n) logm) time, wherem is the number of arcs,n is the number of vertices, andT(m, n) is the time required for solving a maximum flow problem in a network withm arcs andn vertices. In the present paper, taking an approach that is a dual of Tardos's, we also give a strongly polynomial algorithm for the minimum-cost circulation problem. Our algorithm runs in O(m 2 S(m, n) logm) time and reduces the computational complexity, whereS(m, n) is the time required for solving a shortest path problem with a fixed origin in a network withm arcs,n vertices, and a nonnegative arc length function. The complexity is the same as that of Orlin's algorithm, recently developed by efficiently implementing the Edmonds-Karp scaling algorithm.

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  1. Institute of Socio-Economic Planning, University of Tsukuba, 305, Sakura, Ibaraki, Japan

    Satoru Fujishige

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  1. Satoru Fujishige
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Fujishige, S. A capacity-rounding algorithm for the minimum-cost circulation problem: A dual framework of the Tardos algorithm. Mathematical Programming 35, 298–308 (1986). https://doi.org/10.1007/BF01580882

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  • DOI: https://doi.org/10.1007/BF01580882

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