Koucký, M. orcid.org/0000-0003-0808-2269, Rödl, V. and Talebanfard, N. orcid.org/0000-0002-3524-9282 (2021) A separator theorem for hypergraphs and a CSP-SAT algorithm. Logical Methods in Computer Science, 17 (4). 17:1-17:14. ISSN 1860-5974
Abstract
We show that for every r≥2 there exists ϵr>0 such that any r-uniform hypergraph with m edges and maximum vertex degree o(m−−√) contains a set of at most (12−ϵr)m edges the removal of which breaks the hypergraph into connected components with at most m/2 edges. We use this to give an algorithm running in time d(1−ϵr)m that decides satisfiability of m-variable (d,k)-CSPs in which every variable appears in at most r constraints, where ϵr depends only on r and k∈o(m−−√). Furthermore our algorithm solves the corresponding #CSP-SAT and Max-CSP-SAT of these CSPs. We also show that CNF representations of unsatisfiable (2,k)-CSPs with variable frequency r can be refuted in tree-like resolution in size 2(1−ϵr)m. Furthermore for Tseitin formulas on graphs with degree at most k (which are (2,k)-CSPs) we give a deterministic algorithm finding such a refutation.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 M.Koucký, V.Rödl, and N.Talebanfard. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | CSP-SAT; hypergraph; separator; resolution; Tseitin formulas |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 19 Oct 2023 07:57 |
Last Modified: | 19 Oct 2023 07:57 |
Status: | Published |
Publisher: | Centre pour la Communication Scientifique Directe (CCSD) |
Refereed: | Yes |
Identification Number: | 10.46298/lmcs-17(4:17)2021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:204341 |