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Unformatted text preview: satisfaction, including 2cnfs, Horn clauses, causal networks, and boundedwidth 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 ineective, on problems with special structures, like chains and ktrees, having low w3 , directional resolution greatly outperforms DPbacktracking which is one of the most eective satisability algorithm known to date. In conclusion, although directional resolution outperformsy DPbacktracking on some classes of problems, it is not advocated as an eective method for general satisability problems. Even when the structure is right, there are other structureexploiting algorithms, like backjumping, that are likely to be more eective than BDRDP in nding a satisfying solution. What we do advocate is that structurebased components should be integrated, together with other heuristics (like unit propagation), into any algorithm that tries to solve satisability eectively. At the same time, we have shown that, for some structured domains, directional resolution is an eective 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 BenEliyahu 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):177184 (1987). [2] Bertele,U. and Brioschi, F., Nonserial Dynamic Programming, Academic Press, New York, 1972. [3] BenEliyahu, R., and Dechter, R., Default Logic, Propositional Logic and Constraints, in Proceedings of the National Conference on Articial Intelligence (AAAI91), July 1991,
Anaheim, CA, pp. 379385. [4] Crawford, J.M. and Auton, L.D., Experimental Results on the Crossover Point in Satisability Problems, in Proceedings of AAAI93, 1993, pp 2127. [5] Davis, M., Logemann, G., and Loveland D., A Machine Program for Theorem Proving, Communications of the ACM 5:394397 (1962).
[6] Davis, M. and Putnam, H., A Computing Procedure for Quantication Theory, J. ACM 7:201215 (1960). [7] Dechter, R., and Pearl, J. Networkbased Heuristics for Constraint Satisfaction Problems, Articial Intelligence 34:138 (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 Articial Intelligence (IJCAI91), Sidney, Australia, August 1991, pp. 11641170.
[9] Dechter, R., Enhancement Schemes for Constraint Processing: Backjumping, Learning and Cutset Decomposition, Articial Intelligence, 41:273312 (1990). [10] Even, S., Itai, A., and Shamir, A., On the Complexity of Timetable and MultiCommodity Flow", SIAM Jour...
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