Abstract
The efficiency of branch and bound-based algorithms for Max-CSP depends largely on the quality of the available lower bound. An existing approach for lower bound computation aggregates individual contributions of unassigned variables. In this paper, we generalize this approach. Instead of aggregating individual contributions, we aggregate global contributions of disjoint subsets of unassigned variables, which requires a partition of the set of unassigned variables. Using this idea, we introduce the partition-based lower bound, which is superior to previous ones based on individual contributions. Interestingly, this lower bound includes elements already existing in the literature (IC and DAC). We present two algorithms, PFC-PRDAC and PFC-MPRDAC, which are the natural successors of PFC-RDAC and PFC-MRDAC using this new bound. We provide experimental evidence for the superiority of the new algorithms on random problems and real instances of weighted over-constrained problems.
This research is supported by the Spanish CICYT project TIC96-0721-C02-02.
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References
Bistarelli, S., Montanari, U., Rossi, F.: Constraint Solving over Semiring. In: Proc. of the 14th IJCAI, Montreal, Canada (1995)
Cabon, B., de Givry, S., Lobjois, L., Schiex, T., Warners, J.P.: Radio Link Frequency Assignment. Constraints (to appear)
Freuder, E.C., Wallace, R.J.: Partial Constraint Satisfaction. Artificial Intelligence 58, 21–70 (1992)
Larrosa, J., Meseguer, P.: Exploiting the use of DAC in Max-CSP. In: Proc. of the 2nd. CP, Boston, USA (1996)
Larrosa, J., Meseguer, P., Schiex, T.: Maintaining reversible DAC for Max-CSP. Artificial Intelligence 107, 149–163 (1999)
Prosser, P.: Binary Constraint Satisfaction Problems: Some are Harder than Others. In: Proc. of the 11th. ECAI, Amsterdam, The Netherlands (1994)
Schiex, T.: Maximizing the reversible DAC lower bound in Max-CSP is NP-hard. Technical Report 1998/02, INRA (1998)
Schiex, T., Fargier, H., Verfaillie, G.: Valued Constraint Satisfaction Problems: hard and easy problems. In: Proc. of the 14th IJCAI, Montreal, Canada (1995)
Verfaillie, G., Lemaitre, M., Schiex, T.: Russian Doll Search. In: Proc. of the 13th AAAI, Portland, USA (1996)
Wallace, R.: Directed Arc Consistency Preprocessing. In: Meyer, M. (ed.) Constraint Processing. LNCS, vol. 923, pp. 121–137. Springer, Heidelberg (1995)
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Larrosa, J., Meseguer, P. (1999). Partition-Based Lower Bound for Max-CSP. In: Jaffar, J. (eds) Principles and Practice of Constraint Programming – CP’99. CP 1999. Lecture Notes in Computer Science, vol 1713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48085-3_22
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DOI: https://doi.org/10.1007/978-3-540-48085-3_22
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