Fixed Linear Crossing Minimization by Reduction to the Maximum Cut Problem

  • Christoph Buchheim
  • Lanbo Zheng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


Many real-life scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a way that the number of edge crossings is minimized. In this paper, we study a restricted version of the linear layout problem where the order of vertices on the line is fixed, the so-called fixed linear crossing number problem (FLCNP). We show that this \(\mathcal{NP}\)-hard problem can be reduced to the well-known maximum cut problem. The latter problem was intensively studied in the literature; efficient exact algorithms based on the branch-and-cut technique have been developed. By an experimental evaluation on a variety of graphs, we show that using this reduction for solving FLCNP compares favorably to earlier branch-and-bound algorithms.


Integer Linear Program Exact Algorithm Hamiltonian Cycle Cutting Plane Linear Embedding 
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 2006

Authors and Affiliations

  • Christoph Buchheim
    • 1
  • Lanbo Zheng
    • 2
    • 3
  1. 1.Computer Science DepartmentUniversity of CologneGermany
  2. 2.School of Information TechnologiesUniversity of SydneyAustralia
  3. 3.IMAGEN program, National ICTAustralia

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