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Detecting symmetries by branch & cut

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Abstract.

The NP-hard problem of finding symmetries in an abstract graph plays an important role in automatic graph drawing and other applications. In this paper, we present an exact algorithm for automorphism and symmetry detection based on the branch & cut technique. We introduce IP-models for these problems and investigate the structure of the corresponding polytopes. For automorphisms, a complete description of the polytope is derived from a given set of generators of the automorphism group. The rotation polytopes are shown to be related to the asymmetric traveling salesman polytope, while the reflection polytope is related to the matching polytope. The algorithm was implemented within the ABACUS-framework and proves to run fast in practice.

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Authors and Affiliations

  1. Institut für Informatik, Universität zu Köln, Pohligstraße 1, 50969, Köln, Germany

    Christoph Buchheim & Michael Jünger

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  1. Christoph Buchheim
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  2. Michael Jünger
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Correspondence to Michael Jünger.

Additional information

This work was partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

Mathematics Subject Classification (1991): 20B25, 90C10, 90C35

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Buchheim, C., Jünger, M. Detecting symmetries by branch & cut. Math. Program., Ser. B 98, 369–384 (2003). https://doi.org/10.1007/s10107-003-0409-3

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  • DOI: https://doi.org/10.1007/s10107-003-0409-3

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