New algorithms for Exact Satisfiability

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...

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Bibliographic Details
Published in:Theoretical computer science Vol. 332; no. 1; pp. 515 - 541
Main Authors: Byskov, Jesper Makholm, Madsen, Bolette Ammitzbøll, Skjernaa, Bjarke
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 28.02.2005
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Branch-and-reduce algorithm
Computer science; control theory; systems
Exact 3-Satisfiability
Exact Satisfiability
Exact sciences and technology
Exact solution
Exponential-time algorithm
Theoretical computing
Exponential-time algorithm
Exact Satisfiability
Branch-and-reduce algorithm
Exact 3-Satisfiability
Exact solution
Assignment
Computer theory
Satisfiability problem
Algorithm
Exponential time algorithm
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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 ( 2 0.2325 n ) and O ( 2 0.1379 n ) , respectively. The previously best algorithms have running times O ( 2 0.2441 n ) for Exact Satisfiability (Methods Oper. Res. 43 (1981) 419–431) and O ( 2 0.1626 n ) 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.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2004.12.023