{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10490","name":"Hybrid VCSPs with Crisp and Valued Conservative Templates","abstract":"A constraint satisfaction problem (CSP) is a problem of computing a homomorphism R -> G between two relational structures, e.g. between two directed graphs.\r\nAnalyzing its complexity has been a very fruitful research direction, especially for fixed template CSPs (or, non-uniform CSPs), denoted CSP(G),\r\nin which the right side structure G is fixed and the left side structure R is unconstrained. \r\n\r\nRecently, the hybrid setting, written CSP_H(G), where both sides are restricted simultaneously, attracted some attention.\r\nIt assumes that R is taken from a class of relational structures H (called the structural restriction) that additionally is closed under inverse homomorphisms. The last property allows to exploit an algebraic machinery that has been developed for fixed template CSPs. The key concept that connects hybrid CSPs with fixed-template CSPs is the so called lifted language. Namely, this is a constraint language G_R that can be constructed from an input R. The tractability of the language G_R for any input R from H is a necessary condition for the tractability of the hybrid problem.\r\n\r\nIn the first part we investigate templates G for which the latter condition is not only necessary, but also is sufficient. We call such templates G widely tractable. For this purpose, we construct from G a new finite relational structure G' and define a maximal structural restriction H_0 as a class of structures homomorphic to G'.\r\nFor the so called strongly BJK templates that probably captures all templates, we prove that wide tractability is equivalent to the tractability of CSP_{H_0}(G).\r\nOur proof is based on the key observation that R is homomorphic to G' if and only if the core of G_R is preserved by a Siggers polymorphism.\r\nAnalogous result is shown for conservative valued CSPs.","keywords":["constraint satisfaction problem","polymorphisms","algebraic approach","lifted language","hybrid CSPs","closed under inverse homomorphisms"],"author":{"@type":"Person","name":"Takhanov, Rustem","givenName":"Rustem","familyName":"Takhanov"},"position":65,"pageStart":"65:1","pageEnd":"65:13","dateCreated":"2017-12-07","datePublished":"2017-12-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Takhanov, Rustem","givenName":"Rustem","familyName":"Takhanov"},"copyrightYear":"2017","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ISAAC.2017.65","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":["http:\/\/arxiv.org\/abs\/1703.03021","http:\/\/arxiv.org\/abs\/1701.02409","http:\/\/arxiv.org\/abs\/1704.01914"],"isPartOf":{"@type":"PublicationVolume","@id":"#volume6295","volumeNumber":92,"name":"28th International Symposium on Algorithms and Computation (ISAAC 2017)","dateCreated":"2017-12-07","datePublished":"2017-12-07","editor":[{"@type":"Person","name":"Okamoto, Yoshio","givenName":"Yoshio","familyName":"Okamoto"},{"@type":"Person","name":"Tokuyama, Takeshi","givenName":"Takeshi","familyName":"Tokuyama"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10490","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6295"}}}