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Fixed Parameter Algorithms for one-sided crossing minimization Revisited

  • Vida Dujmović
  • Henning Fernau
  • Michael Kaufmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

We exhibit a small problem kernel for the problem one-sided crossing minimization which plays an important role in graph drawing algorithms based on the Sugiyama layering approach. Moreover, we improve on the search tree algorithm developed in [5] and derive an O(1.4656 k  + kn 2) algorithm for this problem, where k upperbounds the number of tolerated crossings of straight lines involved in the drawings of an n-vertex graph. Relations of this graph-drawing problem to the algebraic problem of finding a weighted linear extension of an ordering similar to [7] are exhibited.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vida Dujmović
    • 1
  • Henning Fernau
    • 2
    • 3
  • Michael Kaufmann
    • 2
  1. 1.School of Computer ScienceMcGill UniversityMontreal, QCCanada
  2. 2.WSI für InformatikUniversität TübingenTübingenGermany
  3. 3.School of Electr. and Computer Science, University DriveThe University of NewcastleCallaghanAustralia

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