Branching rules for satisfiability
Tóm tắt
Recent experience suggests that branching algorithms are among the most attractive for solving propositional satisfiability problems. A key factor in their success is the rule they use to decide on which variable to branch next. We attempt to explain and improve the performance of branching rules with an empirical model-building approach. One model is based on the rationale given for the Jeroslow-Wang rule, variations of which have performed well in recent work. The model is refuted by carefully designed computational experiments. A second model explains the success of the Jeroslow-Wang rule, makes other predictions confirmed by experiment, and leads to the design of branching rules that are clearly superior to Jeroslow-Wang.
Tài liệu tham khảo
Amini, M. M. and Racer, M.: A variable-depth-search heuristic for the generalized assignment problem,Management Science, to appear.
Böhm, H.: Report on a SAT Competition, Technical report No. 110, Universität Paderborn, Germany, 1992.
Cook, S. A.: The complexity of theorem-proving procedures, inProc. 3rd Annual ACM Symp. on the Theory of Computing, 1971, pp. 151–158.
Crawford, J.: Problems contributed to DIMACS. For information contact Crawford at AT&T Bell Laboratories, 600 Mountain Ave., Murray Hill, NJ, 07974-0636 USA, e-mail [email protected].
Davis, M. and Putnam, H.: A computing procedure for quantification theory,J. ACM 7 (1960), 201–215.
Dubois, O.: Problems contributed to DIMACS. For information contact Dubois at Laforia, CNRS-Université Paris 6, 4 place Jussieu, 75252 Paris cedex 05, France, e-mail [email protected].
Dubois, O., Andre, P., Boufkhad, Y., and Carlier, J.: SAT versus UNSAT, manuscript, Laforia, CNRS-Université Paris 6, 4 place Jussieu, 75252 Paris cedex 05, France, 1993, e-mail [email protected].
Erdös, P. and Lovász, L.: Problems and results on 3-chromatic hypergraphs and some related questions, inInfinite and Finite Sets, North-Holland, Amsterdam, 1975.
Freeman, T. W.: Failed literals in the Davis-Putnam procedure for SAT, manuscript, Computer and Information Science, University of Pennsylvania, Philadelphia, PA, 19104 USA, CA, 1993, [email protected].
Gallo, G. and Pretolani, D.: A new algorithm for the propositional satisfiability problem, report TR-3/90, Dip. di Informatica, Universitá di Pisa,Discrete Applied Mathematics, to appear.
Gallo, G. and Urbani, G.: Algorithms for testing the satisfiability of propositional formulae,J. Logic programming 7 (1989), 45–61.
Golden, B. L. and Stewart, W. R.: Empirical analysis of heuristics, in Lawler, Lenstra, Rinnooy Kan, and Schmoys (eds),The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley, New York, 1985, pp. 207–249.
Harche, F., Hooker, J. N., and Thompson, G.: A computational study of sastifiability algorithms for propositional logic,ORSA J. Computing 6 (1994), 423–435. For more information contact J. Hooker, email [email protected].
Hooker, J. N.: Needed: An empirical science of algorithms,Operations Research 42 (1994), 201–212.
Hooker, J. N. and Fedjki, C.: Branch and cut solution of inference problems in propositional logic,Annals of Mathematics and AI 1 (1990), 123–139.
Iwama, K., Albeta, H., and Miyano, E.: Random generation of satisfiable and unsatisfiable CNF predicates, inProc. of 12th IFIP World Computer Congress, 1992, pp. 322–328. For further information contact Eiji Miyano, Dept. of Computer Science and Communication Engineering, Kyushu University, Fukuoka 812, Japan, e-mail [email protected].
Jeroslow, R. and Wang, J.: Solving propositional satisfiability problems,Annals of Mathematics and AI 1 (1990), 167–187.
Kamath, A., Karmarkar, N., Ramakrishnan, K., and Resende, M.: A continuous approach to inductive inference,Mathematical Programming 57 (1992), 215–238. For further information contact Mauricio Resende, AT&T Bell Laboratories, Murray Hill, NJ 07974 USA, e-mail [email protected].
Lin, B. W. and Rardin, R. L.: Controlled experimental design for statistical comparison of integer programming algorithms,Management Science 25 (1980), 1258–1271.
Loveland, D. W.:Automated Theorem Proving: A Logical Basis, North-Holland, Amsterdam, 1978.
Mitterreiter, I. and Radermacher, F. J.: Experiments on the running time behavior of some algorithms solving propositional logic problems, manuscript, Forschungsinstitut für anwendungsorientierte Wissensverarbeitung, Ulm, Germany, 1991.
Petersen, R. G.:Design and Analysis of Experiments, Marcel Dekker, New York, 1985.
Pretolani, D.: Efficiency and stability of hypergraph SAT algorithms, manuscript, Dip. di Informatica, Univ. di Pisa, Corso Itali 40, 56125 Pisa, Italy. For information on problems contact e-mail [email protected].
Spencer, J.:Ten Lectures on the Probabilistic Method, Regional Conference Series in Applied Mathematics52, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1987.
Van Gelder, A. and Tsuji, Y. K.: Satisfiability testing with more reasoning and less guessing, manuscript, University of California, Santa Cruz, CA, USA, 1994. For information on problems contact e-mail [email protected] or [email protected].
Wilson, J. M.: Compact normal forms in propositional logic and integer programming formulations,Computers and Operations Research 90 (1990), 309–314.