Abstract
We introduce a novel and exciting research area: symmetrising levels of consistency to produce stronger forms of consistency and more efficient mechanisms for establishing them. We propose new levels of consistency for Constraint Satisfaction Problems (CSPs) incorporating the symmetry group of a CSP. We first define Sym(i,j)-consistency, show that even Sym(1,0)-consistency can prune usefully, and study some consequences of maintaining Sym(i, 0)- consistency. We then present pseudocode for SymPath consistency, and a symmetrised version of singleton consistency, before presenting experimental evidence of these algorithms’ practical effectiveness. With this contribution we establish the study of symmetry-based levels of consistency of CSPs.
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
Flener, P., Frisch, A.M., Hnich, B., Kızıltan, Z., Miguel, I., Pearson, J., Walsh, T.: Breaking row and column symmetries in matrix models. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 462–476. Springer, Heidelberg (2002)
Backofen, R., Will, S.: Excluding symmetries in constraint-based search. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 73–87. Springer, Heidelberg (1999)
Brown, C.A., Finkelstein, L., Purdom Jr., P.W.: Backtrack searching in the presence of symmetry. Nordic Journal of Computing 3(3), 203–219 (1996)
Roney-Dougal, C.M., Gent, I.P., Kelsey, T., Linton, S.A.: Tractable symmetry breaking using restricted search trees. In: Proc. ECAI 2004 (2004)
Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8, 99–118 (1977)
Bessière, C., Régin, J.-C.: Refining the basic constraint propagation algorithm. In: Proc. IJCAI 2001 (2001)
Zhang, Y., Yap, R.H.C.: Making AC-3 an optimal algorithm. In: Proc. IJCAI 2001 (2001)
Gent, I.P., McDonald, I.: Symmetry and propagation: Refining an AC algorithm. In: Proc. SymCon 2003 (2003)
Kelsey, T., Linton, S.A., Roney-Dougal, C.M.: New developments in symmetry breaking in search using computational group theory. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 199–210. Springer, Heidelberg (2004)
Freuder, E.C.: A sufficient condition for backtrack-free search. Journal of the ACM 29(1), 24–32 (1982)
Freuder, E.C.: A sufficient condition for backtrack-bounded search. Journal of the ACM 37(4), 755–761 (1985)
Seress, A.: Permutation group algorithms. Cambridge tracts in mathematics, vol. 152. Cambridge University Press, Cambridge (2002)
Puget, J.-F.: Symmetry breaking using stabilizers. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 585–599. Springer, Heidelberg (2003)
Bessière, C., Régin, J.-C., Yap, R.H.C., Zhang, Y.: An optimal coarse-grained arc consistency algorithm. Artificial Intelligence 165, 165–185 (2005)
Debruyne, R., Bessière, C.: Some practicable filtering techniques for the constraint satisfaction problem. In: Proc. IJCAI 1997, pp. 412–417 (1997)
Barták, R., Erben, R.: A new algorithm for singleton arc consistency. In: Proc. FLAIRS 2004 (2004)
Bessière, C., Debruyne, R.: Optimal and suboptimal singleton arc consistency algorithms. In: Proc. IJCAI 2005 (2005)
Wallace, M.G., Novello, S., Schimpf, J.: ECLiPSe: A platform for constraint logic programming. ICL Systems Journal 12(1), 159–200 (1997)
Gent, I.P., Harvey, W., Kelsey, T.: Groups and constraints: Symmetry breaking during search. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 415–430. Springer, Heidelberg (2002)
Gent, I.P., Harvey, W., Kelsey, T., Linton, S.A.: Generic SBDD using computational group theory. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 333–347. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gent, I.P., Kelsey, T., Linton, S., Roney-Dougal, C. (2005). Symmetry and Consistency. 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_22
Download citation
DOI: https://doi.org/10.1007/11564751_22
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)