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On the p-media polytope of special class of graphs

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  • Mourad Baïou

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Fancisco Barahona

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we consider a well known class of valid inequalities for the p-median and the uncapacitated facility location polytopes, the odd cycle inequalities. It is known that their separation problem is polynomially solvable. We give a new polynomial separation algorithm based on a reduction from the original graph. Then, we define a nontrivial class of graphs, where the odd cycle inequalities together with the linear relaxations of both the p-median and uncapacitated facility location problems, suffice to describe the associated polytope. To do this, we first give a complete description of the fractional extreme points of the linear relaxation for the p-median polytope in that class of graphs.

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  • Mourad Baïou & Fancisco Barahona, 2005. "On the p-media polytope of special class of graphs," Working Papers hal-00242976, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242976
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242976
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    References listed on IDEAS

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    1. Sven de Vries & Marc Posner & Rakesh Vohra, 2003. "Polyhedral Properties of the K -median Problem on a Tree," Discussion Papers 1367, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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