Panolan, F. orcid.org/0000-0001-6213-8687 and Yaghoubizade, H. (2025) On MAX–SAT with Cardinality Constraint. In: Uehara, R., Yamanaka, K. and Yen, H.C., (eds.) WALCOM: Algorithms and Computation. 18th International Conference and Workshops on Algorithms and Computation (WALCOM 2024), 18-20 Mar 2024, Kanazawa, Japan. Lecture Notes in Computer Science, 14549 . Springer , pp. 118-133. ISBN 978-981-97-0566-5
Abstract
We consider the weighted MAX–SAT problem with an additional constraint that at most k variables can be set to true. We call this problem k–WMAX–SAT. This problem admits a (1 − 1/e )-factor approximation algorithm in polynomial time [Sviridenko, Algorithmica 2001] and it is proved that there is no (1 − 1/e + ϵ)-factor approximation algorithm in f (k) · no(k) time for Maximum Coverage, the unweighted monotone version of k–WMAX–SAT [Manurangsi, SODA 2020]. Therefore, we study two restricted versions of the problem in the realm of parameterized complexity.
1. When the input is an unweighted 2–CNF formula (the problem is called k–MAX–2SAT), we design an efficient polynomial-size approximate kernelization scheme. That is, we design a polynomial-time algorithm that given a 2–CNF formula ψ and�ϵ > 0, compresses the input instance to a 2–CNF formula ψ such that any c-approximate solution of ψ� can be converted to a c(1 − ϵ)-approximate solution of ψ in polynomial time.
2. When the input is a planar CNF formula, i.e., the variable-clause incident graph is a planar graph, we show the following results:
– There is an FPT algorithm for k–WMAX–SAT on planar CNF formulas that runs in 2O(k) · (C + V ) time.
– There is a polynomial-time approximation scheme for k– WMAX–SAT on planar CNF formulas that runs in time 2O(1/ϵ ) ·k · (C+V ).
The above-mentioned C and V are the number of clauses and variables of the input formula respectively.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © The Author(s). This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/978-981-97-0566-5_10 |
Keywords: | Parameterized Algorithms; MAX–SAT; MAX–2SAT |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 Nov 2023 10:57 |
Last Modified: | 01 Mar 2025 01:13 |
Published Version: | https://doi.org/10.1007/978-981-97-0566-5 |
Status: | Published |
Publisher: | Springer |
Series Name: | Lecture Notes in Computer Science |
Identification Number: | 10.1007/978-981-97-0566-5_10 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:205928 |