Abstract
We introduce groupoids – generalisations of groups in which not all pairs of elements may be multiplied, or, equivalently, categories in which all morphisms are invertible – as the appropriate algebraic structures for dealing with conditional symmetries in Constraint Satisfaction Problems (CSPs). We formally define the Full Conditional Symmetry Groupoid associated with any CSP, giving bounds for the number of elements that this groupoid can contain. We describe conditions under which a Conditional Symmetry sub-Groupoid forms a group, and, for this case, present an algorithm for breaking all conditional symmetries that arise at a search node. Our algorithm is polynomial-time when there is a corresponding algorithm for the type of group involved. We prove that our algorithm is both sound and complete – neither gaining nor losing solutions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Gent, I.P., McDonald, I., Smith, B.M.: Conditional symmetry in the all-interval series problem. In: Symcon 2003 (2003)
Gent, I.P., McDonald, I., Miguel, I., Smith, B.M.: Approaches to conditional symmetry breaking. In: SymCon 2004 (2004)
Zhang, Y., Freuder, E.C.: Conditional interchangeability and substitutability. In: SymCon 2004 (2004)
Walsh, T.: General symmetry breaking constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 650–664. Springer, Heidelberg (2006)
Brown, R.: From groups to groupoids: A brief survey. Bulletins of the London Mathematical Society 19, 113–134 (1987)
Roney-Dougal, C.M., Gent, I.P., Kelsey, T., Linton, S.A.: Tractable symmetry breaking using restricted search trees. In: ECAI 2004, pp. 211–215 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gent, I.P., Kelsey, T., Linton, S.A., Pearson, J., Roney-Dougal, C.M. (2007). Groupoids and Conditional Symmetry. In: Bessière, C. (eds) Principles and Practice of Constraint Programming – CP 2007. CP 2007. Lecture Notes in Computer Science, vol 4741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74970-7_60
Download citation
DOI: https://doi.org/10.1007/978-3-540-74970-7_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74969-1
Online ISBN: 978-3-540-74970-7
eBook Packages: Computer ScienceComputer Science (R0)