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A polyhedral approach to the multi-layer crossing minimization problem

Extended abstract
  • Michael Jünger
  • Eva K. Lee
  • Petra Mutzel
  • Thomas Odenthal
Planarity and Crossings
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

We study the multi-layer crossing minimization problem from a polyhedral point of view. After the introduction of an integer programming formulation of the multi-layer crossing minimization problem, we examine the 2-layer case and derive several classes of facets of the associated polytope. Preliminary computational results for 2- and 3-layer instances indicate, that the usage of the corresponding facet-defining inequalities in a branch-and-cut approach may only lead to a practically useful algorithm, if deeper polyhedral studies are conducted.

Keywords

Bipartite Graph Integer Program Short Path Problem Integer Programming Formulation Crossing Minimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Michael Jünger
    • 1
  • Eva K. Lee
    • 2
  • Petra Mutzel
    • 3
  • Thomas Odenthal
    • 4
  1. 1.Institut für InformatikUniversität zu KölnGermany
  2. 2.Ind. & Sys. Eng.Georgia Institute of TechnologyUSA
  3. 3.Max-Planck-Institut für InformatikSaarbrücken
  4. 4.Ind. Eng. & Op. Res.Columbia UniversityUSA

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