{"id":"https://openalex.org/W2291107068","doi":"https://doi.org/10.1145/2974019","title":"The Complexity of Finite-Valued CSPs","display_name":"The Complexity of Finite-Valued CSPs","publication_year":2016,"publication_date":"2016-09-21","ids":{"openalex":"https://openalex.org/W2291107068","doi":"https://doi.org/10.1145/2974019","mag":"2291107068"},"language":"en","primary_location":{"id":"doi:10.1145/2974019","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2974019","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1210.2987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082914834","display_name":"Johan Thapper","orcid":null},"institutions":[{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Johan Thapper","raw_affiliation_strings":["Universit\u00e9 Paris-Est Marne-la-Vall\u00e9e, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Est Marne-la-Vall\u00e9e, France","institution_ids":["https://openalex.org/I4210154111"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067656814","display_name":"Stanislav \u017divn\u00fd","orcid":"https://orcid.org/0000-0002-0263-159X"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stanislav \u017divn\u00fd","raw_affiliation_strings":["University of Oxford, Oxford, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082914834"],"corresponding_institution_ids":["https://openalex.org/I4210154111"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0117187,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"4","first_page":"1","last_page":"33"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8170203566551208},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.698269784450531},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5286113619804382},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.5228928923606873},{"id":"https://openalex.org/keywords/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.5000426769256592},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.4662206470966339},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4025813341140747}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8170203566551208},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.698269784450531},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5286113619804382},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.5228928923606873},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.5000426769256592},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.4662206470966339},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4025813341140747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1145/2974019","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2974019","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1210.2987","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.2987","pdf_url":"https://arxiv.org/pdf/1210.2987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.760.5716","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.760.5716","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1210.2987.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01796719v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01796719","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://dl.acm.org/doi/10.1145/2974019","raw_type":"Journal articles"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:9030708d-1cf0-435f-80ad-d591addd1668","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:9030708d-1cf0-435f-80ad-d591addd1668","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:e649b41e-8198-4e97-9027-3dede56daadb","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:e649b41e-8198-4e97-9027-3dede56daadb","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus (http://www.scopus.com/home.url)","raw_type":"Conference"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:e905dfc2-2e55-45a5-b24f-a5cd98d48743","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:e905dfc2-2e55-45a5-b24f-a5cd98d48743","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference item"},{"id":"doi:10.48550/arxiv.1210.2987","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1210.2987","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2291107068","is_oa":false,"landing_page_url":"https://ora.ouls.ox.ac.uk/objects/uuid:e649b41e-8198-4e97-9027-3dede56daadb","pdf_url":null,"source":{"id":"https://openalex.org/S2764889284","display_name":"ORA review team","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"ORA review team","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1210.2987","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.2987","pdf_url":"https://arxiv.org/pdf/1210.2987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2291107068.pdf","grobid_xml":"https://content.openalex.org/works/W2291107068.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W108355652","https://openalex.org/W191485599","https://openalex.org/W655258421","https://openalex.org/W966413371","https://openalex.org/W1877564947","https://openalex.org/W1974691224","https://openalex.org/W1978292808","https://openalex.org/W1979388565","https://openalex.org/W1979514837","https://openalex.org/W1980530521","https://openalex.org/W1983818015","https://openalex.org/W1984074081","https://openalex.org/W1988443389","https://openalex.org/W1996540180","https://openalex.org/W1997649256","https://openalex.org/W1999032440","https://openalex.org/W2005103485","https://openalex.org/W2020154454","https://openalex.org/W2025319967","https://openalex.org/W2026753685","https://openalex.org/W2029110781","https://openalex.org/W2032487621","https://openalex.org/W2034122136","https://openalex.org/W2049143039","https://openalex.org/W2052726983","https://openalex.org/W2063711222","https://openalex.org/W2068190866","https://openalex.org/W2071152266","https://openalex.org/W2071731321","https://openalex.org/W2073279331","https://openalex.org/W2076265075","https://openalex.org/W2091694652","https://openalex.org/W2101712920","https://openalex.org/W2108619558","https://openalex.org/W2110871651","https://openalex.org/W2111739159","https://openalex.org/W2111829945","https://openalex.org/W2114448228","https://openalex.org/W2116407296","https://openalex.org/W2117290960","https://openalex.org/W2119456262","https://openalex.org/W2132104546","https://openalex.org/W2138458087","https://openalex.org/W2138514146","https://openalex.org/W2143238590","https://openalex.org/W2144306116","https://openalex.org/W2146944439","https://openalex.org/W2150339067","https://openalex.org/W2151131175","https://openalex.org/W2151577278","https://openalex.org/W2155683758","https://openalex.org/W2158505527","https://openalex.org/W2159686758","https://openalex.org/W2165967486","https://openalex.org/W2166566648","https://openalex.org/W2168016267","https://openalex.org/W2172276559","https://openalex.org/W2199961663","https://openalex.org/W2950298732","https://openalex.org/W4254380579","https://openalex.org/W4293052541","https://openalex.org/W4388323202"],"related_works":["https://openalex.org/W2151131175","https://openalex.org/W2398609546","https://openalex.org/W2950298732","https://openalex.org/W1603607404","https://openalex.org/W2756790058","https://openalex.org/W107425472","https://openalex.org/W2949796101","https://openalex.org/W3102749561","https://openalex.org/W2158824357","https://openalex.org/W3036972148","https://openalex.org/W2950717240","https://openalex.org/W2496830481","https://openalex.org/W2951224476","https://openalex.org/W2963623916","https://openalex.org/W2799529798","https://openalex.org/W2949623088","https://openalex.org/W2963192233","https://openalex.org/W1556025627","https://openalex.org/W2092436554","https://openalex.org/W2398115706"],"abstract_inverted_index":{"We":[0,56,78],"study":[1],"the":[2,42,95],"computational":[3],"complexity":[4],"of":[5,8,17,44,52,74,103],"exact":[6,64],"minimization":[7],"rational-valued":[9,18],"discrete":[10],"functions.":[11],"Let":[12],"\u0393":[13,84,107],"be":[14],"a":[15,21,26,30,46,50,58,87,109,116],"set":[16,27],"functions":[19,53],"on":[20,72],"fixed":[22],"finite":[23,76],"domain;":[24],"such":[25],"is":[28,41],"called":[29],"finite-valued":[31,68],"constraint":[32,37,69,82],"language":[33,83],".":[34],"The":[35],"valued":[36],"satisfaction":[38],"problem,":[39],"VCSP(\u0393),":[40],"problem":[43],"minimizing":[45],"function":[47],"given":[48],"as":[49],"sum":[51],"from":[54,119],"\u0393.":[55],"establish":[57],"dichotomy":[59],"theorem":[60],"with":[61],"respect":[62],"to":[63,121],"solvability":[65],"for":[66,115],"all":[67],"languages":[70],"defined":[71],"domains":[73],"arbitrary":[75],"size.":[77],"show":[79],"that":[80,113],"every":[81],"either":[85],"admits":[86],"binary":[88],"symmetric":[89],"fractional":[90],"polymorphism,":[91],"in":[92],"which":[93],"case":[94],"basic":[96],"linear":[97],"programming":[98],"relaxation":[99],"solves":[100],"any":[101],"instance":[102],"VCSP(\u0393)":[104],"exactly,":[105],"or":[106],"satisfies":[108],"simple":[110],"hardness":[111],"condition":[112],"allows":[114],"polynomial-time":[117],"reduction":[118],"Max-Cut":[120],"VCSP(\u0393).":[122]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}