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Automatically Exploiting Symmetries in Constraint Programming

  • Conference paper
Recent Advances in Constraints (CSCLP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3419))

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Abstract

We introduce a framework for studying and solving a class of CSP formulations. The framework allows constraints to be expressed as linear and non-linear equations, then compiles them into SAT instances via Boolean logic circuits. While in general reduction to SAT may lead to the loss of structure, we specifically detect several types of structure in high-level input and use them in compilation. Linearity is preserved by the use of pseudo-Boolean (PB) constraints in conjunction with a 0-1 ILP solver that extends common SAT-solving techniques. Symmetries are detected in high-level constraints by solving the graph automorphism problem on parse trees. Symmetry-breaking predicates are added during compilation. Our system generalizes earlier work on symmetries in SAT and 0-1 ILP problems. Empirical evaluation is performed on instances of the social golfers and Hamming code generation problems. We show substantial speedups with symmetry-breaking, especially on unsatisfiable instances. In general, our runtimes with the specialized 0-1 ILP solver Pueblo are competitive with results recently reported for ILOG Solver.

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Authors and Affiliations

  1. Department of EECS, University of Michigan, 1301 Beal Avenue, Ann Arbor, MI, 48109, USA

    Arathi Ramani & Igor L. Markov

Authors
  1. Arathi Ramani
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  2. Igor L. Markov
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Editor information

Editors and Affiliations

  1. Artificial Intelligence Lab, Ecole Polytechnique Fédérale de Lausanne, Station 14, CH-1015, Lausanne, Switzerland

    Boi V. Faltings

  2. Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015, Lausanne, (Switzerland)

    Adrian Petcu

  3. Projet Contraintes, INRIA Rocquencourt, BP105, Domaine de Voluceau, 78153, Le Chesnay Cedex, France

    François Fages

  4. Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Francesca Rossi

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Ramani, A., Markov, I.L. (2005). Automatically Exploiting Symmetries in Constraint Programming. In: Faltings, B.V., Petcu, A., Fages, F., Rossi, F. (eds) Recent Advances in Constraints. CSCLP 2004. Lecture Notes in Computer Science(), vol 3419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11402763_8

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  • DOI: https://doi.org/10.1007/11402763_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25176-7

  • Online ISBN: 978-3-540-32252-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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