Abstract
Usually propagation-based constraint solvers construct a constraint network as a conjunction of constraints. They provide propagators for each form of constraint c. In order to increase expressiveness, systems also usually provide propagators for reified forms of constraints. A reified constraint b ↔ c associates a truth value b with a constraint c. With reified propagators, systems can express complex combinations of constraints using disjunction, implication and negation by flattening. In this paper we argue that reified constraints should be replaced by half-reified constraints of the form b → c. Half-reified constraints do not impose any extra burden on the implementers of propagators compared to unreified constraints, they can implement reified propagators without loss of propagation strength (assuming c is negatable), they extend automatically to global constraints, they simplify the handling of partial functions, and can allow flattening to give better propagation behavior.
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
Achterberg, T., Berthold, T., Koch, T., Wolter, K.: Constraint integer programming: A new approach to integrate CP and MIP. In: Trick, M.A. (ed.) CPAIOR 2008. LNCS, vol. 5015, pp. 6–20. Springer, Heidelberg (2008)
Balas, E.: The prize collecting traveling salesman problem. Networks 19, 621–636 (1989)
Brand, S., Yap, R.: Towards ”Propagation = Logic + Control”. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 102–106. Springer, Heidelberg (2006)
Carlsson, M., Ottosson, G., Carlson, B.: An open-ended finite domain constraint solver. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 191–206. Springer, Heidelberg (1997)
Frisch, A., Stuckey, P.: The proper treatment of undefinedness in constraint languages. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 367–382. Springer, Heidelberg (2009)
Frisch, A.M., Grum, M., Jefferson, C., Hernandez, B.M., Miguel, I.: The design of ESSENCE: A constraint language for specifying combinatorial problems. In: Procs. of IJCAI 2007 (2007)
Jefferson, C., Moore, N.C.A., Nightingale, P., Petrie, K.E.: Implementing logical connectives in constraint programming. Artif. Intell. 174(16-17), 1407–1429 (2010)
Lagerkvist, M.Z., Schulte, C.: Propagator groups. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 524–538. Springer, Heidelberg (2009)
Marriott, K., Nethercote, N., Rafeh, R., Stuckey, P., Garcia de la Banda, M., Wallace, M.: The design of the Zinc modelling language. Constraints 13(3), 229–267 (2008)
Nethercote, N., Stuckey, P., Becket, R., Brand, S., Duck, G., Tack, G.: Minizinc: Towards a standard CP modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007)
Plaisted, D., Greenbaum, S.: A structure-preserving clause form translation. Journal of Symbolic Computation 2, 293–304 (1986)
PSPlib (Project scheduling problem library), http://129.187.106.231/psplib/
Schulte, C.: Programming deep concurrent constraint combinators. In: Pontelli, E., Santos Costa, V. (eds.) PADL 2000. LNCS, vol. 1753, pp. 215–229. Springer, Heidelberg (2000)
Schulte, C., Tack, G.: Views and iterators for generic constraint implementations. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 817–821. Springer, Heidelberg (2005)
Schutt, A., Feydy, T., Stuckey, P., Wallace, M.: Why cumulative decomposition is not as bad as it sounds. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 746–761. Springer, Heidelberg (2009)
Van Hentenryck, P.: The OPL Optimization Programming Language. MIT Press, Cambridge (1999)
Van Hentenryck, P., Saraswat, V., Deville, Y.: Constraint processins in cc(FD) (1991) (manuscript)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feydy, T., Somogyi, Z., Stuckey, P.J. (2011). Half Reification and Flattening. In: Lee, J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23786-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-23786-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23785-0
Online ISBN: 978-3-642-23786-7
eBook Packages: Computer ScienceComputer Science (R0)