New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
A Probabilistic 3-SAT Algorithm Further Improved
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
An Improved Exponential-Time Algorithm for k-SAT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Performance test of local search algorithms using new types of random CNF formulas
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
Local search algorithms for partial MAXSAT
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Adding new clauses for faster local search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
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Recently Schoning has shown that a simple local-search algorithm for 3SAT achieves the currently best upper bound, i.e., an expected time of 1.334^n. In this paper, we show that this algorithm can be modified to run much faster if there is some kind of imbalance in satisfying assignments and we have a (partial) knowledge about that. Especially if a satisfying assignment has imbalanced 0's and 1's, i.e., p"1n 1's and (1-p"1)n 0's, then we can find a solution in time 1.260^n when p"1=13 and 1.072^n when p"1=0.1. Such an imbalance often exists in SAT instances reduced from other problems. As a concrete example, we investigate a reduction from 3DM and show our new approach is nontrivially faster than its direct algorithms. Preliminary experimental results are also given.