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An extension of disjunctive programming and its impact for compact tree formulations

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  • STEPHAN, Rüdiger

    () (Université catholique de Louvain,CORE, B-1348 Louvain-la-Neuve, Belgium)

Abstract

In the 1970’s, Balas [2, 4] introduced the concept of disjunctive programming, which is optimization over unions of polyhedra. One main result of his theory is that, given linear descriptions for each of the polyhedra to be taken in the union, one can easily derive an extended formulation of the convex hull of the union of these polyhedra. In this paper, we give a generalization of this result by extending the polyhedral structure of the variables coupling the polyhedra taken in the union. Using this generalized concept, we derive polynomial size linear programming formulations (compact formulations) of a well- known spanning tree approximation of Steiner trees and flow equivalent trees for node- as well as edge- capacitated undirected networks. We also present a compact formulation for Gomory-Hu trees, and, as a consequence, of the minimum T-cut problem (but not for the associated T-cut polyhedron). Recently, Kaibel and Loos [10] introduced a more involved framework called polyhedral branching systems to derive extended formulations. The most of our model can be expressed in terms of their framework. The value of our model can be seen in the fact that it completes their framework with an interesting algorithmic aspect.

Suggested Citation

  • STEPHAN, Rüdiger, 2010. "An extension of disjunctive programming and its impact for compact tree formulations," CORE Discussion Papers 2010045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2010045
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    File URL: http://www.uclouvain.be/cps/ucl/doc/core/documents/coredp2010_45web.pdf
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    References listed on IDEAS

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    1. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
    2. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
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    Keywords

    disjunctive programming; compact formulation; flow-equivalent trees; Gomory-Hu trees;

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