Abstract
We introduce a new method for excluding symmetries in constraint based search. To our knowledge, it is the first declarative method that can be applied to arbitrary symmetries. Our method is based on the notion of symmetric constraints, which are used in our modification of a general constraint based search algorithm. The method does not influence the search strategy. Furthermore, it can be used with either the full set of symmetries, or with an subset of all symmetries.
We proof correctness, completeness and symmetry exclusion properties of our method. We then show how to apply the method in the special case of geometric symmetries (rotations and reflections) and permutation symmetries. Furthermore, we give results from practical applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aguirre, A.S.M.: How to use symmetries in boolean constraint solving. In: Benhamou, F., Colmerauer, A. (eds.) Constraint Logic Programming, Selected Research, ch. 16, pp. 287–306. The MIT Press, Cambridge (1993)
Backofen, R.: Constraint techniques for solving the protein structure prediction problem. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, p. 72. Springer, Heidelberg (1998)
Benhamou, B.: Study of symmetry in constraint satisfaction problems. In: Borning, A. (ed.) PPCP 1994. LNCS, vol. 874. Springer, Heidelberg (1994)
Benhamou, B., Sais, L.: Tractability through symmetries in propositional calculus. Journal of Automated Reasoning 12, 89–102 (1994)
Crawford, J.M., Ginsberg, M., Luks, E., Roy, A.: Symmetry breaking predicates for search problems. In: Proc. of the 5th International Conference on Principles of Knowledge Representation and Reasoning (KR 1996), pp. 149–159 (1996)
de la Tour, T.B.: Minimizing the number of clauses by renaming. In: Stickel, M.E. (ed.) CADE 1990. LNCS, (LNAI) vol. 449, pp. 558–572. Springer, Heidelberg (1990)
Eugene Freuder. Eliminating interchangeable values in constraint satisfaction problems. In Proc. of AAAI’91, pages 227–233, 1991.
Gent, I.P., Smith, B.: Symmetry breaking during search in constraint programming. Report 99.02. University of Leeds (January 1999)
Schulte, C., Smolka, G., Würtz, J.: Encapsulated search and constraint programming in Oz. In: Borning, A.H. (ed.) PPCP 1994. LNCS, vol. 874, pp. 134–150. Springer, Heidelberg (1994)
Smolka, G.: The Oz programming model. In: van Leeuwen, J. (ed.) Computer Science Today. LNCS, vol. 1000, pp. 324–343. Springer, Heidelberg (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Backofen, R., Will, S. (1999). Excluding Symmetries in Constraint-Based Search. In: Jaffar, J. (eds) Principles and Practice of Constraint Programming – CP’99. CP 1999. Lecture Notes in Computer Science, vol 1713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48085-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-48085-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66626-4
Online ISBN: 978-3-540-48085-3
eBook Packages: Springer Book Archive