Faster exact solutions for some NP-hard problems
Theoretical Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Algorithms for four variants of the exact satisfiability problem
Theoretical Computer Science
Exact 3-Satisfiability Is Decidable in Time O(20.16254n)
Annals of Mathematics and Artificial Intelligence
An algorithm for exact satisfiability analysed with the number of clauses as parameter
Information Processing Letters
On Some SAT-Variants over Linear Formulas
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
An algorithm for Exact Satisfiability analysed with the number of clauses as parameter
Information Processing Letters
Partition into triangles on bounded degree graphs
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Algorithms for max hamming exact satisfiability
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Complexity results for linear XSAT-Problems
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
The worst-case upper bound for exact 3-satisfiability with the number of clauses as the parameter
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
XSAT and NAE-SAT of linear CNF classes
Discrete Applied Mathematics
| Hi-index | 5.23 |
The Exact Satisfiability problem is to determine if a CNF-formula has a truth assignment satisfying exactly one literal in each clause; Exact 3-Satisfiability is the version in which each clause contains at most three literals. In this paper, we present algorithms for Exact Satisfiability and Exact 3-Satisfiability running in time O(20.2325n) and O(20.1379n), respectively. The previously best algorithms have running times O(20.2441n) for Exact Satisfiability (Methods Oper. Res. 43 (1981) 419-431) and O(20.1626n) for Exact 3-Satisfiability (Annals of Mathematics and Artificial Intelligence 43 (1) (2005) 173-193 and Zapiski nauchnyh seminarov POMI 293 (2002) 118-128). We extend the case analyses of these papers and observe that a formula not satisfying any of our cases has a small number of variables, for which we can try all possible truth assignments and for each such assignment solve the remaining part of the formula in polynomial time.