Abstract
WCSP is an optimization problem for which many forms of soft local (arc) consistencies have been proposed such as, for example, existential directional arc consistency (EDAC) and virtual arc consistency (VAC). In this paper, we adopt a different perspective by revisiting the well-known property of (soft) substitutability. First, we provide a clear picture of the relationships existing between soft neighborhood substitutability (SNS) and a tractable property called pcost which allows us to compare the cost of two values (through the use of so-called cost pairs). We prove that under certain assumptions, pcost is equivalent to SNS but weaker than SNS in the general case since we show that SNS is coNP-hard. We also show that SNS preserves the property VAC but not the property EDAC. Finally, we introduce an algorithm to enforce pcost that benefits from several optimizations (early breaks, residues, timestamping). The practical interest of maintaining pcost together with AC*, FDAC or EDAC, during search. is shown on various series of WCSP instances.
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References
Bistarelli, S., Faltings, B., Neagu, N.: Interchangeability in Soft CSPs. In: O’Sullivan, B. (ed.) Constraint Solving and CLP. LNCS (LNAI), vol. 2627, pp. 31–46. Springer, Heidelberg (2003)
Bistarelli, S., Montanari, U., Rossi, F., Schiex, T., Verfaillie, G., Fargier, H.: Semiring-based CSPs and valued CSPs: Frameworks, properties, and comparison. Constraints 4(3), 199–240 (1999)
Choueiry, B.Y., Faltings, B., Weigel, R.: Abstraction by interchangeability in resource allocation. In: Proceedings of IJCAI 1995, pp. 1694–1710 (1995)
Cooper, M.C.: Reduction operations in fuzzy or valued constraint satisfaction. Fuzzy Sets and Systems 134(3), 311–342 (2003)
Cooper, M.C., de Givry, S., Sanchez, M., Schiex, T., Zytnicki, M.: Virtual arc consistency for weighted CSP. In: Proceedings of AAAI 2008, pp. 253–258 (2008)
Cooper, M.C., de Givry, S., Sanchez, M., Schiex, T., Zytnicki, M., Werner, T.: Soft arc consistency revisited. Artificial Intelligence 174(7-8), 449–478 (2010)
Cooper, M.C.: Fundamental properties of neighbourhood substitution in constraint satisfaction problems. Artificial Intelligence 90, 1–24 (1997)
de Givry, S.: Singleton consistency and dominance for weighted CSP. In: Proceedings of CP 2004 Workshop on Preferences and Soft Constraints (2004)
de Givry, S., Heras, F., Zytnicki, M., Larrosa, J.: Existential arc consistency: Getting closer to full arc consistency in weighted CSPs. In: Proceedings of IJCAI 2005, pp. 84–89 (2005)
Freuder, E.C.: Eliminating interchangeable values in constraint satisfaction problems. In: Proceedings of AAAI 1991, pp. 227–233 (1991)
Haselbock, A.: Exploiting interchangeabilities in constraint satisfaction problems. In: Proceedings of IJCAI 1993, pp. 282–287 (1993)
Karakashian, S., Woodward, R., Choueiry, B., Prestwhich, S., Freuder, E.: A partial taxonomy of substitutability and interchangeability. Technical Report arXiv:1010.4609, CoRR (2010)
Koster, A.M.: Frequency assignment: Models and Algorithms. PhD thesis, University of Maastricht, The Netherlands (1999)
Lal, A., Choueiry, B.Y., Freuder, E.C.: Neighborhood interchangeability and dynamic bundling for non-binary finite CSPs. In: Proceedings of AAAI 2005, pp. 397–404 (2005)
Larrosa, J.: Node and arc consistency in weighted CSP. In: Proceedings of AAAI 2002, pp. 48–53 (2002)
Larrosa, J., Schiex, T.: Solving weighted CSP by maintaining arc consistency. Artificial Intelligence 159(1-2), 1–26 (2004)
Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley (1990)
Schiex, T., Fargier, H., Verfaillie, G.: Valued constraint satisfaction problems: Hard and easy problems. In: Proceedings of IJCAI 1995, pp. 631–639 (1995)
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Lecoutre, C., Roussel, O., Dehani, D.E. (2012). WCSP Integration of Soft Neighborhood Substitutability. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_31
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DOI: https://doi.org/10.1007/978-3-642-33558-7_31
Publisher Name: Springer, Berlin, Heidelberg
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