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Packing and covering with integral feasible flows in integral supply-demand networks

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Abstract

Polynomial-time algorithms are presented for solving combinatorial packing and covering problems defined from the integral feasible flows in an integral supply-demand network. These algorithms are also shown to apply to packing and covering problems defined by the minimal integral solutions to general totally unimodular systems. Analogous problems arising from matroid bases are also discussed and it is demonstrated that a means for solving such problems is provided by recent work of Cunningham.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Rice University, Houston, TX, USA

    R. E. Bixby

  2. Département de mathématiques et d'informatique, Université du Québec à Montréal, Montréal, Canada

    O. M. -C. Marcotte

  3. School of OR&IE, Cornell University, Ithaca, NY, USA

    L. E. Trotter Jr.

Authors
  1. R. E. Bixby
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  2. O. M. -C. Marcotte
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  3. L. E. Trotter Jr.
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Additional information

Research partially supported by NSF grant MCS81-05Z327 at Northwestern University, and by the Alexander von Humboldt Foundation and the Institut für Okonometrie und Operations Research der Universität Bonn (Federal Republic of Germany), while the author was on leave from Rice University.

Research partially supported by NSERCC grant A9126 and by NSF grants ECS-8005350 and ECS-8113534 to Cornell University

Research partially supported by NSF grants ECS-8113534 and ECS-8504077.

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Bixby, R.E., Marcotte, O.M.C. & Trotter, L.E. Packing and covering with integral feasible flows in integral supply-demand networks. Mathematical Programming 39, 231–239 (1987). https://doi.org/10.1007/BF02592074

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  • DOI: https://doi.org/10.1007/BF02592074

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