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Vertex-Disjoint Packing of Two Steiner Trees: Polyhedra and Branch-and-Cut

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Integer Programming and Combinatorial Optimization (IPCO 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1610))

Abstract

Consider the problem of routing the electrical connections among two large terminal sets in circuit layout. A realistic model for this problem is given by the vertex-disjoint packing of two Steiner trees (2VPST), which is known to be NP-complete. This work presents an investigation on the 2VPST polyhedra. The main idea is to depart from facet-defining inequalities for a vertex-weighted Steiner tree polyhedra. Some of these inequalities are proven to also define facets for the packing polyhedra, while others are lifted to derive new important families of inequalities, including proven facets. Separation algorithms are also presented. The resulting branch-and-cut code has an excellent performance and is capable of solving problems on grid graphs with up to 10000 vertices and 5000 terminals in a few minutes.

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References

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Author information

Authors and Affiliations

  1. Departamento de Informática, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente, 225, Rio de Janeiro RJ, 22453-900, Brasil

    Eduardo Uchoa & Marcus Poggi de Aragão

Authors
  1. Eduardo Uchoa
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  2. Marcus Poggi de Aragão
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Editor information

Editors and Affiliations

  1. GSIA, Carnegie Mellon University, Schenley Park, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rainer E. Burkard  & Gerhard J. Woeginger  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Uchoa, E., Poggi de Aragão, M. (1999). Vertex-Disjoint Packing of Two Steiner Trees: Polyhedra and Branch-and-Cut. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_33

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  • DOI: https://doi.org/10.1007/3-540-48777-8_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66019-4

  • Online ISBN: 978-3-540-48777-7

  • eBook Packages: Springer Book Archive

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