Exact Crossing Minimization

  • Christoph Buchheim
  • Dietmar Ebner
  • Michael Jünger
  • Gunnar W. Klau
  • Petra Mutzel
  • René Weiskircher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


The crossing number of a graph is the minimum number of edge crossings in any drawing of the graph into the plane. This very basic property has been studied extensively in the literature from a theoretic point of view and many bounds exist for a variety of graph classes. In this paper, we present the first algorithm able to compute the crossing number of general sparse graphs of moderate size and present computational results on a popular benchmark set of graphs. The approach uses a new integer linear programming formulation of the problem combined with strong heuristics and problem reduction techniques. This enables us to compute the crossing number for 91 percent of all graphs on up to 40 nodes in the benchmark set within a time limit of five minutes per graph.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christoph Buchheim
    • 1
  • Dietmar Ebner
    • 2
  • Michael Jünger
    • 1
  • Gunnar W. Klau
    • 3
  • Petra Mutzel
    • 4
  • René Weiskircher
    • 5
  1. 1.Department of Computer ScienceUniversity of Cologne 
  2. 2.Institute of Computer Graphics and AlgorithmsVienna University of Technology 
  3. 3.Department of Mathematics and Computer ScienceFU Berlin 
  4. 4.Department of Computer ScienceUniversity of Dortmund 
  5. 5.CSIRO Mathematical and Information Sciences 

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