A separator theorem for hypergraphs and a CSP-SAT algorithm
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00551098" target="_blank" >RIV/67985840:_____/21:00551098 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/21:10438303
Result on the web
<a href="https://doi.org/10.46298/lmcs-17(4:17)2021" target="_blank" >https://doi.org/10.46298/lmcs-17(4:17)2021</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46298/lmcs-17(4:17)2021" target="_blank" >10.46298/lmcs-17(4:17)2021</a>
Alternative languages
Result language
angličtina
Original language name
A separator theorem for hypergraphs and a CSP-SAT algorithm
Original language description
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.
Czech name
—
Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
1860-5974
Volume of the periodical
17
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
14
Pages from-to
17
UT code for WoS article
000744066500008
EID of the result in the Scopus database
2-s2.0-85123311375