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A strongly polynomial algorithm for the transportation problem

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Abstract

For the (linear) transportation problem withm supply nodes,n demand nodes andk feasible arcs we describe an algorithm which runs in time proportional tom logm(k + n logn) (assuming w.l.o.g.m⩾n). The algorithm uses excess scaling. The complexity bound is a slight improvement over the bound achieved by an application of a min-cost-flow algorithm of Orlin to the transportation problem.

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Authors and Affiliations

  1. Wirtschaftswissenschaftliche Fakultät, Universität Passau, Innstrasse 29, D-94030, Passau, Germany

    P. Kleinschmidt

  2. Westdeutsche Landesbank, Mathematische Beratung, D-40217, Düsseldorf, Germany

    H. Schannath

Authors
  1. P. Kleinschmidt
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  2. H. Schannath
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Corresponding author. Research supported in part by grant no. I-84-095.06/88 of the German—Israeli-Foundation for Scientific Research and Development.

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Kleinschmidt, P., Schannath, H. A strongly polynomial algorithm for the transportation problem. Mathematical Programming 68, 1–13 (1995). https://doi.org/10.1007/BF01585755

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  • DOI: https://doi.org/10.1007/BF01585755

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