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Branch-Cut-and-Propagate for the Maximum k-Colorable Subgraph Problem with Symmetry

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Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6697))

Abstract

Given an undirected graph and a positive integer k, the maximum k-colorable subgraph problem consists of selecting a k-colorable induced subgraph of maximum cardinality. The natural integer programming formulation for this problem exhibits two kinds of symmetry: arbitrarily permuting the color classes and/or applying a non-trivial graph automorphism gives equivalent solutions. It is well known that such symmetries have negative effects on the performance of constraint/integer programming solvers.

We investigate the integration of a branch-and-cut algorithm for solving the maximum k-colorable subgraph problem with constraint propagation techniques to handle the symmetry arising from the graph. The latter symmetry is handled by (non-linear) lexicographic ordering constraints and linearizations thereof. In experiments, we evaluate the influence of several components of our algorithm on the performance, including the different symmetry handling methods. We show that several components are crucial for an efficient algorithm; in particular, the handling of graph symmetries yields a significant performance speed-up.

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Author information

Authors and Affiliations

  1. Cork Constraint Computation Centre, Computer Science Department, University College Cork, Ireland

    Tim Januschowski

  2. Institute for Mathematical Optimization, TU Braunschweig, Pockelsstr. 14, 38106, Braunschweig, Germany

    Marc E. Pfetsch

Authors
  1. Tim Januschowski
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  2. Marc E. Pfetsch
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Editor information

Editors and Affiliations

  1. Zuse Institut Berlin, Takustr. 7, 14195, Berlin, Germany

    Tobias Achterberg

  2. Department of Computer Science, University of Toronto, 5 King’s College Rd., M5S 3G8, Toronto, ON, Canada

    J. Christopher Beck

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Januschowski, T., Pfetsch, M.E. (2011). Branch-Cut-and-Propagate for the Maximum k-Colorable Subgraph Problem with Symmetry. In: Achterberg, T., Beck, J.C. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2011. Lecture Notes in Computer Science, vol 6697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21311-3_11

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  • DOI: https://doi.org/10.1007/978-3-642-21311-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21310-6

  • Online ISBN: 978-3-642-21311-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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