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The permutahedron ofN-sparse posets

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Abstract

The permutahedron of a poset is the convex hull of all incidence vectors of linear extensions. For the case ofN-sparse posets in which any five elements induce at most oneN we give a characterization of the permutahedron in terms of linear inequalities. This yields an LP-solution for minimizing the weighted mean completion time for jobs with unit processing times andN-sparse precedence constraints. We close with an extension of our approach to arbitrary processing times.

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Author notes

  1. Yaoguang Wang

    Present address: Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

Authors and Affiliations

  1. Institut für Informatik, University of Cologne, D-50969, Köln, Germany

    Annelie von Arnim & Rainer Schrader

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ont., Canada

    Yaoguang Wang

Authors
  1. Annelie von Arnim
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  2. Rainer Schrader
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  3. Yaoguang Wang
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von Arnim, A., Schrader, R. & Wang, Y. The permutahedron ofN-sparse posets. Mathematical Programming 75, 1–18 (1996). https://doi.org/10.1007/BF02592204

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  • DOI: https://doi.org/10.1007/BF02592204

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