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Makes three main contributions first we revive the

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Unformatted text preview: satisfaction, including 2-cnfs, Horn clauses, causal networks, and bounded-width networks. Second, we identify new tractable classes based on the notion of diversity . Third, our empirical tests show that, while on uniform theories directional resolution is indeed ine ective, on problems with special structures, like chains and k-trees, having low w3 , directional resolution greatly outperforms DP-backtracking which is one of the most e ective satis ability algorithm known to date. In conclusion, although directional resolution outperformsy DP-backtracking on some classes of problems, it is not advocated as an e ective method for general satis ability problems. Even when the structure is right, there are other structure-exploiting algorithms, like backjumping, that are likely to be more e ective than BDR-DP in nding a satisfying solution. What we do advocate is that structure-based components should be integrated, together with other heuristics (like unit propagation), into any algorithm that tries to solve satis ability e ectively. At the same time, we have shown that, for some structured domains, directional resolution is an e ective knowledge compilation procedure, compiling knowledge into a form that facilitates ecient model generation and query processing. 29 Acknowledgements We would like to thank Dan Frost, Eddie Schwalb and Rachel Ben-Eliyahu for comments on this paper. Also we would like to thank Dan Frost for running experiments with the backjumping algorithm. 30 References [1] Arnborg, S., Corneil D.G., and Proskurowski A., Complexity of Finding Embedding in a k -tree, SIAM J. Algebraic Discrete Methods 8(2):177-184 (1987). [2] Bertele,U. and Brioschi, F., Nonserial Dynamic Programming, Academic Press, New York, 1972. [3] Ben-Eliyahu, R., and Dechter, R., Default Logic, Propositional Logic and Constraints, in Proceedings of the National Conference on Arti cial Intelligence (AAAI-91), July 1991, Anaheim, CA, pp. 379-385. [4] Crawford, J.M. and Auton, L.D., Experimental Results on the Cross-over Point in Satis ability Problems, in Proceedings of AAAI-93, 1993, pp 21-27. [5] Davis, M., Logemann, G., and Loveland D., A Machine Program for Theorem Proving, Communications of the ACM 5:394-397 (1962). [6] Davis, M. and Putnam, H., A Computing Procedure for Quanti cation Theory, J. ACM 7:201-215 (1960). [7] Dechter, R., and Pearl, J. Network-based Heuristics for Constraint Satisfaction Problems, Arti cial Intelligence 34:1-38 (1987). [8] Dechter, R., and Pearl, J., Directed Constraint Networks: A Relational Framework for Causal Models, in Proceedings of the Twelfth International Joint Conference on Arti cial Intelligence (IJCAI-91), Sidney, Australia, August 1991, pp. 1164-1170. [9] Dechter, R., Enhancement Schemes for Constraint Processing: Backjumping, Learning and Cutset Decomposition, Arti cial Intelligence, 41:273-312 (1990). [10] Even, S., Itai, A., and Shamir, A., On the Complexity of Timetable and MultiCommodity Flow", SIAM Jour...
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