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Unformatted text preview: nal on Computing, 5:691-703 (1976). 31 [11] Freuder, E.C., A Sucient Condition for Backtrack-Free Search, J. ACM, 29:24-32 (1982). [12] Galil, Z., On the Complexity of Regular Resolution and the Davis-Putnam Procedure, Theoretical Computer Science 4:23-46 (1977). [13] Gashnig, J., Performance Measurement and Analysis of Certain Search Algorithms, Technical Report CMU-CS-79-124, Carnegie Mellon University, 1979. [14] Goerdt, A., Davis-Putnam Resolution Versus Unrestricted Resolution, Annals of Math- ematics and Arti cial Intelligence, 6:169-184 (1992). [15] Goldberg, A., Purdom P., and Brown, C., Average Time Analysis of Simpli ed DavisPutnam Procedures, Information Processing Letters, 15:72-75 (1982). [16] McAllester, D., Private communication. [17] Mitchell, D., Selman, B., and Levesque, H., Hard and Easy Distributions of SAT Problems, in Proceedings of AAAI-92, 1992, pp. 459-465. [18] Seidel, R., A New Method for Solving Constraint Satisfaction Problems, in Proceed- ings of the Seventh international joint conference on Arti cial Intelligence (IJCAI-81), Vancouver, Canada, August 1981, pp. 338-342. [19] Selman, B., Levesque H., and Mitchell, D., A New Method for Solving Hard Satis ability Problems, in Proceedings of the Tenth National Conference on Arti cial Intelligence (AAAI-92), San Jose, CA, July 1992. [20] Lauritzen, S.L. and Spigelholter, D.J., Local Computations With Probabilities on Graphical Structures and Their Applications to Expert Systems, Journal of the Royal Statistical Society, Series, B, 5:65-74 (1988). [21] van Beek, P. and Dechter, R., On the Minimality and Decomposability of Row-Convex Constraint Networks, Journal of the Association of Computing Machinery (JACM), In press, 1995. 32 [22] van Beek, P. and Dechter, R., Constraint Tightness vs Global Consistency, November, 1994. Submitted manuscript. 33 Table 5: BDR-DP (bound 3) and DP-backtracking (termination at 20000 deadends) on (k; m)-trees Mean values on 50 experiments per each row DP-backtracking Time: 1st solution Dead ends Time BDR only BDR-DP with bound=3 Time: 1st solution Dead ends Number of new clauses DP after BDR DP after BDR 1-4-tree, Nclauses = 11, Ncliques = 100 Total: 401 variable, 1100 clauses 233.2 7475 5.4 17.7 2 298 1-4-tree, Nclauses = 12, Ncliques = 100 Total: 401 variable, 1200 clauses 352.5 10547 7.5 1.2 7 316 1-4-tree, Nclauses = 14, Ncliques = 100 Total: 401 variable, 1400 clauses 1-4-tree, Nclauses = 13, Ncliques = 100 Total: 401 variable, 1300 clauses 328.8 9182 9.8 0.25 3 339 1-4-tree, Nclauses = 14, Ncliques = 100 Total: 401 variable, 1400 clauses 174.2 4551 11.9 0.0 0 329 2-4-tree, Nclauses = 12, Ncliques = 100 Total: 402 variable, 1200 clauses 160.0 4633 6.0 1.6 25 341 2-4-tree, Nclauses = 13, Ncliques = 100 Total: 402 variable, 1300 clauses 95.4 2589 8.3 34 0.1 0 390 Table 6: Query processing on a 3-cnf chain (20 subtheories, 5 variables in each) 20 queries of length 1 DP before DR 0.1 0.0 224.2 296.2 240.5 34.1 34.0 0.0 313.0 362.0 0.1 362.8 361.2 0.0 0.7 363.0 68.1 295.5 0.0 367.4 13 1 30811 40841 33234 4753 4754 1 43324 50001 14 50001 50001 1 91 50001 9505 40842 1 50001 DP afterDR 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Time Deadends Time Deadends 35...
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