Dreier, J., Ordyniak, S. orcid.org/0000-0003-1935-651X and Szeider, S. (2023) CSP Beyond Tractable Constraint Languages. Constraints, 28 (3). pp. 450-471. ISSN 1383-7133
Abstract
The constraint satisfaction problem (CSP) is among the most studied computational problems. While NP-hard, many tractable subproblems have been identified (Bulatov 2017, Zhuk 2017) Backdoors, introduced by Williams, Gomes, and Selman (2003), gradually extend such a tractable class to all CSP instances of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a CSP instance and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021) for SAT, is a more refined distance measure, which admits the parallel utilization of different backdoor variables. Bounded backdoor size implies bounded backdoor depth, but there are instances of constant backdoor depth and arbitrarily large backdoor size. Dreier, Ordyniak, and Szeider (2022) provided fixed-parameter algorithms for finding backdoors of small depth into the classes of Horn and Krom formulas. In this paper, we consider backdoor depth for CSP. We consider backdoors w.r.t. tractable subproblems CΓ of the CSP defined by a constraint language Γ, i.e., where all the constraints use relations from the language Γ. Building upon Dreier et al.’s game-theoretic approach and their notion of separator obstructions, we show that for any finite, tractable, semi-conservative constraint language Γ, the CSP is fixed-parameter tractable parameterized by the backdoor depth into CΓ plus the domain size. With backdoors of low depth, we reach classes of instances that require backdoors of arbitrary large size. Hence, our results strictly generalize several known results for CSP that are based on backdoor size.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | CSP, backdoor depth, constraint language, tractable class, recursive backdoor |
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: | 04 Oct 2023 15:06 |
Last Modified: | 29 Nov 2023 12:32 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10601-023-09362-3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:203895 |