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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
First Online:
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 
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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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