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CONSTRAINTS
2006

Symmetry Definitions for Constraint Satisfaction Problems

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Symmetry Definitions for Constraint Satisfaction Problems
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.
David A. Cohen, Peter Jeavons, Christopher Jeffers
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where CONSTRAINTS
Authors David A. Cohen, Peter Jeavons, Christopher Jefferson, Karen E. Petrie, Barbara M. Smith
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