Dreier, J., Ordyniak, S. orcid.org/0000-0003-1935-651X and Szeider, S. (Cover date: June 2024) SAT Backdoors: Depth Beats Size. Journal of Computer and System Sciences, 142. 103520. ISSN 0022-0000
Abstract
For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 1984). Backdoors, introduced by Williams, Gomes and Selman (2003), gradually extend such a tractable class to all formulas of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a formula and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021), is a more refined distance measure, which admits the utilization of different backdoor variables in parallel. We propose FPT approximation algorithms to compute backdoor depth into the classes Horn and Krom. This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | SAT; Satisfiability; Backdoor; Elimination distance; Parameterized algorithms |
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) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/V00252X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Jan 2024 13:44 |
Last Modified: | 02 Feb 2024 16:20 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jcss.2024.103520 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208015 |