Abstract
Symmetry Breaking During Search (SBDS) adds conditional symmetry breaking constraints (which are nogoods) dynamically upon backtracking to avoid exploring symmetrically equivalents of visited search space. The constraint store is proliferated with numerous such individual nogoods which are weak in constraint propagation. We introduce the notion of increasing nogoods, and give a global constraint of a sequence of increasing nogoods, incNGs. Reasoning globally with increasing nogoods allows extra prunings. We prove formally that nogoods accumulated for a given symmetry at a search node in SBDS and its variants are increasing. Thus we can maintain only one increasing-nogoods global constraint for each given symmetry during search. We give a polynomial time filtering algorithm for incNGs and also an efficient incremental counterpart which is stronger than GAC on each individual nogood. We demonstrate with extensive experimentation how incNGs can increase propagation and speed up search against SBDS, its variants, SBDD and carefully tailored static methods.
We thank the anonymous referees and Toby Walsh for their kind and insightful comments and patience.
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.
References
Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry breaking predicates for search problems. In: KR 1996, pp. 148–159 (1996)
Dechter, R.: Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition. Artificial Intelligence, 273–312 (1990)
Fahle, T., Schamberger, S., Sellmann, M.: Symmetry breaking. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 93–107. Springer, Heidelberg (2001)
Flener, P., Frisch, A.M., Hnich, B., Kiziltan, 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. 187–192. Springer, Heidelberg (2002)
Flener, P., Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Matrix modelling. In: ModRef 2001 (2001)
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.: Generic SBDD using computational group theory. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 333–347. Springer, Heidelberg (2003)
Gent, I., Smith, B.: Symmetry breaking in constraint programming. In: ECAI 2000, pp. 599–603 (2000)
Gent, I.P., Walsh, T.: CSPlib: A benchmark library for constraints. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 480–481. Springer, Heidelberg (1999)
Hnich, B., Prestwich, S.D., Selensky, E., Smith, B.M.: Constraint models for the covering test problem. Constraints, 199–219 (2006)
Law, Y.C., Lee, J.: Global constraints for integer and set value precedence. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 362–376. Springer, Heidelberg (2004)
Lee, J., Zhu, Z.: Boosting SBDS for partial symmetry breaking in constraint programming. In: AAAI 2014 (to appear, 2014)
Mackworth, A.: Consistency in networks of relations. Artificial Intelligence, 99–118 (1977)
Mears, C., de la Banda, M.G., Demoen, B., Wallace, M.: Lightweight dynamic symmetry breaking. Constraints, 1–48 (2013)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient sat solver. In: DAC 2001, pp. 530–535 (2001)
Petrie, K.E., Smith, B.M.: Symmetry breaking in graceful graphs. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 930–934. Springer, Heidelberg (2003)
Puget, J.: Breaking symmetries in all different problems. In: IJCAI 2005, pp. 272–277 (2005)
Puget, J.F.: On the satisfiability of symmetrical constrained satisfaction problems. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 350–361. Springer, Heidelberg (1993)
Roney-Dougal, C.M., Gent, I.P., Kelsey, T., Linton, S.: Tractable symmetry breaking using restricted search trees. In: ECAI 2004, pp. 211–215 (2004)
Rossi, F., Van Beek, P., Walsh, T.: Handbook of constraint programming. Elsevier (2006)
Zhang, L., Malik, S.: The quest for efficient boolean satisfiability solvers. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 17–36. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Lee, J.H.M., Zhu, Z. (2014). An Increasing-Nogoods Global Constraint for Symmetry Breaking During Search. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_35
Download citation
DOI: https://doi.org/10.1007/978-3-319-10428-7_35
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10427-0
Online ISBN: 978-3-319-10428-7
eBook Packages: Computer ScienceComputer Science (R0)