A separator theorem for hypergraphs and a CSP-SAT algorithm

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11320/21:10438303

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A separator theorem for hypergraphs and a CSP-SAT algorithm

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

A separator theorem for hypergraphs and a CSP-SAT algorithm

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GX19-27871X" target="_blank" >GX19-27871X: Efektivní aproximační algoritmy a obvodová složitost</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

1860-5974

Svazek periodika

17

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

14

Strana od-do

17

Kód UT WoS článku

000744066500008

EID výsledku v databázi Scopus

2-s2.0-85123311375