Algebraic Approach to Promise Constraint Satisfaction

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10437966" target="_blank" >RIV/00216208:11320/21:10437966 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=iVYyRwPgHZ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=iVYyRwPgHZ</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3457606" target="_blank" >10.1145/3457606</a>

Result language

angličtina

Original language name

Algebraic Approach to Promise Constraint Satisfaction

Original language description

The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the past 20 years. A new version of the CSP, the promise CSP (PCSP), has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring. The PCSP significantly extends the standard decision CSP. The complexity of CSPs with a fixed constraint language on a finite domain has recently been fully classified, greatly guided by the algebraic approach, which uses polymorphisms-high-dimensional symmetries of solution spaces-to analyse the complexity of problems. The corresponding classification for PCSPs is wide open and includes some long-standing open questions, such as the complexity of approximate graph colouring, as special cases. The basic algebraic approach to PCSP was initiated by Brakensiek and Guruswami, and in this article, we significantly extend it and lift it from concrete properties of polymorphisms to their abstract properties. We introduce a new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem and show that every PCSP with a fixed constraint language is equivalent to a problem of this form. This allows us to identify a &quot;measure of symmetry&quot; that is well suited for comparing and relating the complexity of different PCSPs via the algebraic approach. We demonstrate how our theory can be applied by giving both general and specific hardness/tractability results. Among other things, we improve the state-of-the-art in approximate graph colouring by showing that, for any k &gt;= 3, it is NP-hard to find a (2k - 1)-colouring of a given k-colourable graph.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

R - Projekt Ramcoveho programu EK

Publication year

2021

Confidentiality

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

Name of the periodical

Journal of the ACM

ISSN

0004-5411

e-ISSN

—

Volume of the periodical

68

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

66

Pages from-to

1-66

UT code for WoS article

000744649100007

EID of the result in the Scopus database

2-s2.0-85122597501