Almost 2-SAT is fixed-parameter tractable
We consider the following problem. Given a 2- cnf formula, is it possible to remove at most k clauses so that the resulting 2- cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but- k 2-SAT, 2- cnf de...
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| Veröffentlicht in: | Journal of computer and system sciences Jg. 75; H. 8; S. 435 - 450 |
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| Sprache: | Englisch |
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01.12.2009
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| ISSN: | 0022-0000, 1090-2724 |
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| Abstract | We consider the following problem. Given a 2-
cnf formula, is it possible to remove at most
k clauses so that the resulting 2-
cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but-
k 2-SAT, 2-
cnf deletion, and 2-SAT deletion. The status of the fixed-parameter tractability of this problem is a long-standing open question in the area of parameterized complexity. We resolve this open question by proposing an algorithm that solves this problem in
O
(
15
k
×
k
×
m
3
)
time showing that this problem is fixed-parameter tractable. |
|---|---|
| AbstractList | We consider the following problem. Given a 2-
cnf formula, is it possible to remove at most
k clauses so that the resulting 2-
cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but-
k 2-SAT, 2-
cnf deletion, and 2-SAT deletion. The status of the fixed-parameter tractability of this problem is a long-standing open question in the area of parameterized complexity. We resolve this open question by proposing an algorithm that solves this problem in
O
(
15
k
×
k
×
m
3
)
time showing that this problem is fixed-parameter tractable. |
| Author | Razgon, Igor O'Sullivan, Barry |
| Author_xml | – sequence: 1 givenname: Igor surname: Razgon fullname: Razgon, Igor email: i.razgon@cs.ucc.ie – sequence: 2 givenname: Barry surname: O'Sullivan fullname: O'Sullivan, Barry email: b.osullivan@cs.ucc.ie |
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| Cites_doi | 10.1093/comjnl/bxm056 10.1006/jagm.1998.0996 10.1093/comjnl/bxm040 10.1007/978-3-540-73951-7_43 10.1145/1374376.1374404 10.1007/11427186_22 10.1007/978-3-540-73420-8_33 10.1016/j.orl.2003.10.009 10.1007/978-3-540-73951-7_37 10.1007/978-3-540-39658-1_44 10.1016/j.tcs.2005.10.007 10.1007/978-3-540-77120-3_25 10.1016/S0304-3975(01)00414-5 10.1016/j.dam.2003.03.002 10.1007/11611257_28 |
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| Snippet | We consider the following problem. Given a 2-
cnf formula, is it possible to remove at most
k clauses so that the resulting 2-
cnf formula is satisfiable? This... |
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| SubjectTerms | Fixed-parameter algorithms Satisfiability problems Separation problems |
| Title | Almost 2-SAT is fixed-parameter tractable |
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