Detecting Symmetries by Branch & Cut

  • Christoph Buchheim
  • Michael Jünger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)


We present a new approach for detecting automorphisms and symmetries of an arbitrary graph based on branch & cut. We derive an IP-model for this problem and have a first look on cutting planes and primal heuristics. The algorithm was implemented within the ABACUS framework; its experimental runtimes are promising.


Integer Linear Program Maximum Clique Valid Inequality Node Label Arbitrary Graph 
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.


  1. 1.
    O. Bastert. New ideas for canonically computing graph algebras. Technical Report TUM-M9803, Technische Universität München, Fakultät für Mathematik, 1998.Google Scholar
  2. 2.
    P. Eades and X. Lin. Spring algorithms and symmetry. Theoretical Computer Science, 240(2):379–405, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    H. de Fraysseix. An heuristic for graph symmetry detection. In J. Kratochvíl, editor, Graph Drawing’ 99, volume 1731 of Lecture Notes in Computer Science, pages 276–285. Springer-Verlag, 1999.CrossRefGoogle Scholar
  4. 4.
    S.-H. Hong, P. Eades, and S.-H. Lee. Finding planar geometric automorphisms in planar graphs. In K.-Y. Chwa et al., editors, Algorithms and computation. 9th international symposium, ISAAC’ 98, volume 1533 of Lecture Notes in Computer Science, pages 277–286. Springer-Verlag, 1998.CrossRefGoogle Scholar
  5. 5.
    M. Jünger and S. Thienel. The ABACUS system for branch-and-cut-and-pricealgorithms in integer programming and combinatorial optimization. Software — Practice & Experience, 30(11):1325–1352, 2000.zbMATHCrossRefGoogle Scholar
  6. 6.
    J. Manning. Computational complexity of geometric symmetry detection in graphs. In Great Lakes Computer Science Conference, volume 507 of Lecture Notes in Computer Science, pages 1–7. Springer-Verlag, 1990.Google Scholar
  7. 7.
    H. Purchase. Which aesthetic has the greatest effect on human understanding? In Giuseppe Di Battista, editor, Graph Drawing’ 97, volume 1353 of Lecture Notes in Computer Science, pages 248–261. Springer-Verlag, 1997.CrossRefGoogle Scholar
  8. 8.
    R. C. Read and D. G. Corneil. The graph isomorphism disease. Journal of Graph Theory, 1:339–363, 1977.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Christoph Buchheim
    • 1
  • Michael Jünger
    • 1
  1. 1.Universität zu Köln, Institut für InformatikKölnGermany

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