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On the parameterized complexity of (k,s)-SAT.

Paulusma, D. and Szeider, S. (2019) 'On the parameterized complexity of (k,s)-SAT.', Information processing letters., 43 . pp. 34-36.


Let (k, s)-SAT be the k-SAT problem restricted to formulas in which each variable occurs in at most s clauses. It is well known that (3, 3)-SAT is trivial and (3, 4)-SAT is NP-complete. Answering a question posed by Iwama and Takaki (DMTCS 1997), Berman, Karpinski and Scott (DAM 2007) gave, for every fixed t ≥ 0, a polynomial-time algorithm for (3, 4)-SAT restricted to formulas in which the number of variables that occur in four clauses is t. Parameterized by t, their algorithm runs in XP time. We extend their result by giving, for every k ≥ 3 and s ≥ k, an FPT algorithm for (k, s)-SAT when parameterized by the number t of variables occurring in more than k clauses.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:13 November 2018
Date deposited:29 November 2018
Date of first online publication:16 November 2018
Date first made open access:16 November 2019

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