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PACE Solver Description: OCMu64, a Solver for One-Sided Crossing Minimization

Authors Ragnar Groot Koerkamp , Mees de Vries

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Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
  • Theory of computation → Computational geometry
Keywords
  • Graph drawing
  • crossing number
  • branch and bound

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Abstract

Given a bipartite graph (A,B), the one-sided crossing minimization (OCM) problem is to find an ordering of the vertices of B that minimizes the number of edge crossings when drawn in the plane.
We introduce the novel strongly fixed, practically fixed, and practically glued reductions that maximally generalize some existing reductions. We apply these in our exact solver OCMu64, that directly uses branch-and-bound on the ordering of the vertices of B and does not depend on ILP or SAT solvers.

Cite As Get BibTex

Ragnar Groot Koerkamp and Mees de Vries. PACE Solver Description: OCMu64, a Solver for One-Sided Crossing Minimization. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 35:1-35:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.IPEC.2024.35

Author Details

Ragnar Groot Koerkamp
  • ETH Zurich, Switzerland
Mees de Vries
  • Unaffiliated, The Netherlands

Supplementary Materials

References

  1. Vida Dujmovic, Henning Fernau, and Michael Kaufmann. Fixed parameter algorithms for one-sided crossing minimization revisited. Journal of Discrete Algorithms, 6(2):313-323, June 2008. URL: https://doi.org/10.1016/j.jda.2006.12.008.
  2. Vida Dujmovic and Sue Whitesides. An efficient fixed parameter tractable algorithm for 1-sided crossing minimization. Algorithmica, 40(1):15-31, April 2004. URL: https://doi.org/10.1007/s00453-004-1093-2.
  3. P. Eades and N.C. Wormald. The Median Heuristic for Drawing 2-layered Networks. Technical report. University of Queensland, Department of Computer Science, 1986. Google Scholar
  4. Peter Eades and David Kelly. Heuristics for reducing crossings in 2-layered networks. Ars Combinatoria, 21(A):89-98, 1986. Google Scholar
  5. Peter Eades and Nicholas C. Wormald. Edge crossings in drawings of bipartite graphs. Algorithmica, 11(4):379-403, April 1994. URL: https://doi.org/10.1007/bf01187020.
  6. Ragnar Groot Koerkamp and Mees de Vries. OCMu64. Software (visited on 2024-11-28). URL: https://github.com/mjdv/ocmu64, URL: https://doi.org/10.4230/artifacts.22525.
  7. Ragnar Groot Koerkamp and Mees de Vries. OCMu64. Software (visited on 2024-11-28). URL: https://doi.org/10.5281/zenodo.11671980.
  8. Erkki Mäkinen. Experiments on drawing 2-level hierarchical graphs. International Journal of Computer Mathematics, 36(3-4):175-181, January 1990. URL: https://doi.org/10.1080/00207169008803921.
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