Abstract
Propagation based solvers typically represent variables by a current domain of possible values that may be part of a solution. Finite set variables have been considered impractical to represent as a domain of possible values since, for example, a set variable ranging over subsets of {1, ..., N} has 2N possible values. Hence finite set variables are presently represented by a lower bound set and upper bound set, illustrating all values definitely in (and by negation) all values definitely out. Propagators for finite set variables implement set bounds propagation where these sets are further constrained. In this paper we show that it is possible to represent the domains of finite set variables using reduced ordered binary decision diagrams (ROBDDs) and furthermore we can build efficient domain propagators for set constraints using ROBDDs. We show that set domain propagation is not only feasible, but can solve some problems significantly faster than using set bounds propagation because of the stronger propagation.
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
Azevedo, F., Barahona, P.: Modelling digital circuits problems with set constraints. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 414–428. Springer, Heidelberg (2000)
Bessiére, C., Régin, J.-C.: Arc consistency for general constraint networks: preliminary results. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI 1997), pp. 398–404 (1997)
Bryant, R.: Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24(3), 293–318 (1992)
Gervet, C.: Interval propagation to reason about sets: Definition and implenentation of a practical language. Constraints 1(3), 191–244 (1997)
Kirkman, T.P.: On a problem in combinatorics. Cambridge and Dublin Math. Journal, 191–204 (1847)
Kiziltan, Z.: Symmetry Breaking Ordering Constraints. PhD thesis, Uppsala University (2004)
Marriott, K., Stuckey, P.J.: Programming with Constraints: an Introduction. MIT Press, Cambridge (1998)
Müller, T.: Constraint Propagation in Mozart. PhD thesis, Universität des Saarlandes, Naturwissenschaftlich-Technische Fakultät I, Fachrichtung Informatik (2001)
Puget, J.-F.: PECOS: A high level constraint programming language. In: Proceedings of SPICIS 1992 (1992)
Sadler, A., Gervet, C.: Global reasoning on sets. In: FORMUL 2001 workshop on modelling and problem formulation (2001)
Somogyi, Z., Henderson, F., Conway, T.: The execution algorithm of Mercury, an efficient purely declarative logic programming language. JLP 29(1-3), 17–64 (1996)
Van Hentenryck, P., Saraswat, V., Deville, Y.: Design, implementation, and evaluation of the constraint language cc(FD). JLP 37(1-3), 139–164 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lagoon, V., Stuckey, P.J. (2004). Set Domain Propagation Using ROBDDs. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-30201-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23241-4
Online ISBN: 978-3-540-30201-8
eBook Packages: Springer Book Archive