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A Global k-Level Crossing Reduction Algorithm

  • Christian Bachmaier
  • Franz J. Brandenburg
  • Wolfgang Brunner
  • Ferdinand Hübner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)

Abstract

Directed graphs are commonly drawn by the Sugiyama algorithm, where crossing reduction is a crucial phase. It is done by repeated one-sided 2-level crossing minimizations, which are still \({\mathcal{NP}}\)-hard.

We introduce a global crossing reduction, which at any particular time captures all crossings, especially for long edges. Our approach is based on the sifting technique and improves the level-by-level heuristics in the hierarchic framework by a further reduction of the number of crossings by 5 – 10%. In addition it avoids type 2 conflicts which help to straighten the edges, and has a running time which is quadratic in the size of the input graph independently of dummy vertices. Finally, the approach can directly be extended to cyclic, radial, and clustered level graphs where it achieves similar improvements over the previous algorithms.

Keywords

Outer Segment Input Graph Binary Decision Diagram Local View Global Median 
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 2010

Authors and Affiliations

  • Christian Bachmaier
    • 1
  • Franz J. Brandenburg
    • 1
  • Wolfgang Brunner
    • 1
  • Ferdinand Hübner
    • 1
  1. 1.University of PassauGermany

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