Fat-trees: universal networks for hardware-efficient supercomputing
IEEE Transactions on Computers
Journal of the ACM (JACM)
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Efficient parallel solution of linear systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Artificial intelligence (3rd ed.)
Artificial intelligence (3rd ed.)
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parallelism in random access machines
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A fast parallel algorithm for the maximal independent set problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Constraint Processing
The intractability of resolution (complexity)
The intractability of resolution (complexity)
Graph dissection techniques for vlsi and algorithms
Graph dissection techniques for vlsi and algorithms
Computational Aspects of VLSI
Principles of Constraint Programming
Principles of Constraint Programming
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Many well-known problems in Artificial Intelligence can be formulated in terms of systems of constraints. The problem of testing the satisfiability of propositional formulae (SAT) is of special importance due to its numerous applications in theoretical computer science and Artificial Intelligence. A brute-force algorithm for SAT will have exponential time complexity O(2^n), where n is the number of Boolean variables of the formula. Unfortunately, more sophisticated approaches such as resolution result in similar performances in the worst case. In this paper, we present a simple and relatively efficient parallel divide-and-conquer method to solve various subclasses of SAT. The dissection stage of the parallel algorithm splits the original formula into smaller subformulae with only a bounded number of interacting variables. In particular, we derive a parallel algorithm for the class of formulae whose corresponding graph representation is planar. Our parallel algorithm for planar 3-SAT has the worst-case performance of 2^O^(^n^) on a PRAM (parallel random access model) computer. Applications of our method to constraint satisfaction problems are discussed.