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A bad network problem for the simplex method and other minimum cost flow algorithms

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Abstract

For any integern, a modified transportation problem with 2n + 2 nodes is constructed which requires 2n + 2n−2−2 iterations using all but one of the most commonly used minimum cost flow algorithms.

As a result, the Edmonds—Karp Scaling Method [3] becomes the only known “good” (in the sense of Edmonds) algorithm for computing minimum cost flows.

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA

    Norman Zadeh

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  1. Norman Zadeh
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Zadeh, N. A bad network problem for the simplex method and other minimum cost flow algorithms. Mathematical Programming 5, 255–266 (1973). https://doi.org/10.1007/BF01580132

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  • DOI: https://doi.org/10.1007/BF01580132

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