Dreier, J, Ordyniak, S orcid.org/0000-0003-1935-651X and Szeider, S (2022) CSP Beyond Tractable Constraint Languages. In: Solnon, C, (ed.) Proceedings of 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). 28th International Conference on Principles and Practice of Constraint Programming (CP 2022), 31 Jul - 05 Aug 2022, Haifa, Israel. Leibniz International Proceedings in Informatics (LIPIcs), 235 . Schloss Dagstuhl , 20:1-20:17. ISBN 978-3-95977-240-2
Abstract
The constraint satisfaction problem (CSP) is among the most studied computational problems. While NP-hard, many tractable subproblems have been identified (Bulatov 2017, Zuk 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: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © Jan Dreier, Sebastian Ordyniak, and Stefan Szeider. This is an open access conference paper under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
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: | 20 May 2022 13:08 |
Last Modified: | 07 Aug 2023 10:36 |
Status: | Published |
Publisher: | Schloss Dagstuhl |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Identification Number: | 10.4230/LIPIcs.CP.2022.20 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:187109 |