A fast parallel SAT-solver — efficient workload balancing

We present a fast parallel SAT-solver on a message based MIMD machine. The input formula is dynamically divided into disjoint subformulas. Small subformulas are solved by a fast sequential SAT-solver running on every processor, which is based on the Davis-Putnam procedure with a special heuristic for variable selection. The algorithm uses optimized data structures to modify Boolean formulas. Additionally efficient workload balancing algorithms are used, to achieve a uniform distribution of workload among the processors. We consider the communication network topologiesd-dimensional processor grid and linear processor array. Tests with up to 256 processors have shown very good efficiency-values (>0.95).

[1]  Ewald Speckenmeyer,et al.  Is Average Superlinear Speedup Possible? , 1988, CSL.

[2]  Paul Walton Purdom,et al.  Backtracking and probing , 1996, Satisfiability Problem: Theory and Applications.

[3]  Armin Haken,et al.  The Intractability of Resolution , 1985, Theor. Comput. Sci..

[4]  G. S. Tseitin.  On the Complexity of Derivation in Propositional Calculus , 1983 .

[5]  Ewald Speckenmeyer,et al.  Solving satisfiability in less than 2n steps , 1985, Discret. Appl. Math..

[6]  Alan M. Frieze,et al.  Analysis of Two Simple Heuristics on a Random Instance of k-SAT , 1996, J. Algorithms.

[7]  Toby Walsh,et al.  Towards an Understanding of Hill-Climbing Procedures for SAT , 1993, AAAI.

[8]  O. Dubois.  Can a very simple algorithm be efficient for solving the SAT problem , 1993 .

[9]  Yannis C. Stamatiou,et al.  Approximating the unsatisfiability threshold of random formulas , 1998, Random Struct. Algorithms.

[10]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[11]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[12]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[13]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[14]  Ming-Te Chao,et al.  Probabilistic Analysis of Two Heuristics for the 3-Satisfiability Problem , 1986, SIAM J. Comput..

[15]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[16]  James M. Crawford,et al.  Experimental Results on the Crossover Point inSatis ability , 1993 .

[17]  John V. Franco,et al.  Elimination of Infrequent Variables Improves Average Case Performance of Satisfiability Algorithms , 1991, SIAM J. Comput..