Abstract
A Non-binary Constraint Satisfaction Problem (CSP) can be solved by converting the problem into an equivalent binary one and applying well-established binary CSP techniques. An alternative way is to use extended versions of binary techniques directly on the non-binary problem. There are two well-known computational methods in the literature for translating a non-binary CSP to an equivalent binary CSP; (i) the hidden variable encoding and (ii) the dual encoding. In this paper we make a theoretical and empirical study of arc consistency for the binary encodings. An arc consistency algorithm for the hidden variable encoding with optimal O(ekd k) worst-case time complexity is presented. This algorithm is compared theoretically and empirically to an optimal generalized arc consistency algorithm that operates on the non-binary representation. We also describe an arc consistency algorithm for the dual encoding with O(e 2 d k) worst-case complexity. This gives an O(d k) reduction compared to a generic arc consistency algorithm. Both theoretical and computational results show that the encodings are competitive with the non-binary representation for certain classes of non-binary CSPs.
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References
Bacchus, F., Van Beek, P.: On the Conversion between Non-Binary and Binary Constraint Satisfaction Problems. In: Proceedings of AAAI 1998, pp. 310–318 (1998)
Bacchus, F., Chen, X., van Beek, P., Walsh, T.: Binary vs. Non-Binary CSPs. Artificial Intelligence (2002)
Beacham, A., Chen, X., Sillito, J., Van Beek, P.: Constraint Programming Lessons Learned from Crossword Puzzles. In: Proceedings of the 14th Canadian Conference in AI 2001, Canada (2001)
Bessière, C., Freuder, E.C., Régin, J.C.: Using Inference to reduce Arc Consistency Computation. In: Proceedings of IJCAI 1995, pp. 592–599 (1995)
Bessière, C., Meseguer, P., Freuder, E.C., Larrosa, J.: On Forward Checking for Non-binary Constraint Satisfaction. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 88–102. Springer, Heidelberg (1999)
Bessière, C., Régin, J.C.: Refining the basic constraint propagation algorithm. In: Proceedings of IJCAI 2001 (2001)
Dechter, R., Pearl, J.: Tree Clustering for Constraint Networks. Artificial Intelligence 38, 353–366 (1989)
Ginsberg, M., Frank, M., Halpin, M., Torrance, M.: Search Lessons learned from Crossword Puzzles. In: Proceedings of AAAI 1990, pp. 210–215 (1990)
Van Hentenryck, P., Deville, Y., Teng, C.: A Generic Arc Consistency Algorithm and its specializations. Artificial Intelligence 57, 291–321 (1992)
Mamoulis, N., Stergiou, K.: Solving non-binary CSPs using the Hidden Variable Encoding. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, p. 168. Springer, Heidelberg (2001)
Miguel, I., Shen, Q.: Solution Techniques for Constraint Satisfaction Problems: Foundations. Artificial Intelligence Review 15, 243–267 (2001)
Mhor, R., Masini, G.: Arc and Path Consistency revisited. Artificial Intelligence 28, 225–233 (1986)
Rossi, F., Petrie, C., Dhar, V.: On the equivalence of constraint satisfaction problems. In: Proceedings of ECAI 1990, pp. 550–556 (1990)
Stergiou, K., Walsh, T.: Encodings of Non-Binary Constraint Satisfaction Problems. In: Proceedings of AAAI 1999, pp. 163–168 (1999)
Zhang, Y., Yap, R.: Making AC-3 an optimal algorithm. In: Proceedings of IJCAI 2001 (2001)
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Samaras, N., Stergiou, K. (2004). Arc Consistency in Binary Encodings of Non-binary CSPs: Theoretical and Experimental Evaluation. In: Vouros, G.A., Panayiotopoulos, T. (eds) Methods and Applications of Artificial Intelligence. SETN 2004. Lecture Notes in Computer Science(), vol 3025. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24674-9_37
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DOI: https://doi.org/10.1007/978-3-540-24674-9_37
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