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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| Vydáno v: | Theoretical computer science Ročník 332; číslo 1; s. 515 - 541 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
28.02.2005
Elsevier |
| Témata: | |
| ISSN: | 0304-3975, 1879-2294 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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
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(
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. |
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| ISSN: | 0304-3975 1879-2294 |
| DOI: | 10.1016/j.tcs.2004.12.023 |