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Symmetry Definitions for Constraint Satisfaction Problems

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 3709)

Abstract

We review the many different definitions of symmetry for constraint satisfaction problems (CSPs) that have appeared in the literature, and show that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as an operation preserving the constraints. We refer to these as solution symmetries and constraint symmetries. We define a constraint symmetry more precisely as an automorphism of a hypergraph associated with a CSP instance, the microstructure complement. We show that the solution symmetries of a CSP instance can also be obtained as the automorphisms of a related hypergraph, the k-ary nogood hypergraph and give examples to show that some instances have many more solution symmetries than constraint symmetries. Finally, we discuss the practical implications of these different notions of symmetry.

Keywords

  • Symmetry Group
  • Automorphism Group
  • Constraint Programming
  • Constraint Satisfaction Problem
  • Bijective Mapping

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.

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Cohen, D., Jeavons, P., Jefferson, C., Petrie, K.E., Smith, B.M. (2005). Symmetry Definitions for Constraint Satisfaction Problems. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_5

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  • DOI: https://doi.org/10.1007/11564751_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29238-8

  • Online ISBN: 978-3-540-32050-0

  • eBook Packages: Computer ScienceComputer Science (R0)