Abstract
Among, Common and Disjoint are global constraints useful in modelling problems involving resources. We study a number of variations of these constraints over integer and set variables. We show how computational complexity can be used to determine whether achieving the highest level of consistency is tractable. For tractable constraints, we present a polynomial propagation algorithm and compare it to logical decompositions with respect to the amount of constraint propagation. For intractable cases, we show in many cases that a propagation algorithm can be adapted from a propagation algorithm of a similar tractable one.
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References
Beldiceanu, N.: Pruning for the minimum constraint family and for the number of distinct values constraint family. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 211–224. Springer, Heidelberg (2001)
Beldiceanu, N.: Global constraints as graph properties on a structured network of elementary constraints of the same type. Technical report T2000/01, Swedish Institute of Computer Science (2000)
Beldiceanu, N., Contegean, E.: Introducing global constraints in CHIP. Mathematical Computer Modelling 20(12), 97–123 (1994)
Beldiceanu, N., Katriel, I., Thiel, S.: Filtering algorithms for the same and usedby constraints. MPI Technical Report MPI-I-2004-1-001 (2004)
Bessiere, C., Hebrard, E., Hnich, B., Walsh, T.: The Complexity of Global Constraints. In: Proc. of AAAI 2004, AAAI Press / The MIT Press (2004)
Bessiere, C., Hebrard, E., Hnich, B., Kizilitan, Z., Walsh, T.: The Range and Roots Constraints: Specifying Counting and Occurrence Problems. In: Proc. of IJCAI 2005, pp. 60–65. Professional Book Center (2005)
Cheng, B.M.W., Choi, K.M.F., Lee, J.H.M., Wu, J.C.K.: Increasing Constraint Propagation by Redundant Modeling: an Experience Report. Constraints 4(2), 167–192 (1999)
Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proc. of AAAI 1994, pp. 362–367. AAAI Press, Menlo Park (1994)
Régin, J.-C.: Generalized arc consistency for global cardinality constraints. In: Proc. of AAAI 1996, pp. 209–215. AAAI Press / The MIT Press (1996)
Sadler, A., Gervet, C.: Global reasoning on sets. In: Proc. of Workshop on Modelling and Problem Formulation (FORMUL 2001), Held alongside CP (2001)
Swedish Institue of Computer Science, SICStus Prolog User’s Manual, Release 3.12.0 (2004), available at http://www.sics.se/sicstus/docs/latest/pdf/sicstus.pdf
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Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T. (2006). Among, Common and Disjoint Constraints. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds) Recent Advances in Constraints. CSCLP 2005. Lecture Notes in Computer Science(), vol 3978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11754602_3
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DOI: https://doi.org/10.1007/11754602_3
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