{"id":"https://openalex.org/W2747084554","doi":"https://doi.org/10.1145/3091528","title":"On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances","display_name":"On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances","publication_year":2017,"publication_date":"2017-07-31","ids":{"openalex":"https://openalex.org/W2747084554","doi":"https://doi.org/10.1145/3091528","mag":"2747084554"},"language":"en","primary_location":{"id":"doi:10.1145/3091528","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3091528","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"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":"ACM Transactions on Computational Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068702258","display_name":"Ronald de Haan","orcid":"https://orcid.org/0000-0003-2023-0586"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Ronald De Haan","raw_affiliation_strings":["Algorithms and Complexity Group, TU Wien, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity Group, TU Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009111693","display_name":"Iyad Kanj","orcid":"https://orcid.org/0000-0003-1698-8829"},"institutions":[{"id":"https://openalex.org/I118353179","display_name":"DePaul University","ror":"https://ror.org/04xtx5t16","country_code":"US","type":"education","lineage":["https://openalex.org/I118353179"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Iyad Kanj","raw_affiliation_strings":["School of Computing, DePaul University, Chicago, IL, United States"],"affiliations":[{"raw_affiliation_string":"School of Computing, DePaul University, Chicago, IL, United States","institution_ids":["https://openalex.org/I118353179"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037092803","display_name":"Stefan Szeider","orcid":"https://orcid.org/0000-0001-8994-1656"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Stefan Szeider","raw_affiliation_strings":["Algorithms and Complexity Group, TU Wien, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity Group, TU Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068702258"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1441608,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"3","first_page":"1","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9966999888420105,"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":0.9851999878883362,"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.840991735458374},{"id":"https://openalex.org/keywords/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.7207960486412048},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.6270321011543274},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.6189034581184387},{"id":"https://openalex.org/keywords/conjunctive-normal-form","display_name":"Conjunctive normal form","score":0.5502328276634216},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5484583377838135},{"id":"https://openalex.org/keywords/true-quantified-boolean-formula","display_name":"True quantified Boolean formula","score":0.5464460253715515},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.525428056716919},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4687851667404175},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45401492714881897},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.45068684220314026},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.43857666850090027},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.41598784923553467},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3958895802497864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35338616371154785},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20808321237564087},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06923419237136841}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.840991735458374},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.7207960486412048},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.6270321011543274},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6189034581184387},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.5502328276634216},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5484583377838135},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.5464460253715515},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.525428056716919},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4687851667404175},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45401492714881897},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.45068684220314026},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.43857666850090027},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.41598784923553467},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3958895802497864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35338616371154785},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20808321237564087},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06923419237136841},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3091528","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3091528","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"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":"ACM Transactions on Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/7c229384-d41c-4195-92d6-1b5e24f18dd6","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/on-the-parameterized-complexity-of-finding-small-unsatisfiable-subsets-of-cnf-formulas-and-csp-instances(7c229384-d41c-4195-92d6-1b5e24f18dd6).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"de Haan, R, Kanj, I & Szeider, S 2017, 'On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances', ACM Transactions on Computational Logic, vol. 18, no. 3, 21. https://doi.org/10.1145/3091528","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dare.uva.nl:publications/7c229384-d41c-4195-92d6-1b5e24f18dd6","is_oa":false,"landing_page_url":"http://dare.uva.nl/personal/pure/en/publications/on-the-parameterized-complexity-of-finding-small-unsatisfiable-subsets-of-cnf-formulas-and-csp-instances(7c229384-d41c-4195-92d6-1b5e24f18dd6).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"de Haan, R, Kanj, I & Szeider, S 2017, 'On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances', ACM Transactions on Computational Logic, vol. 18, no. 3, 21. https://doi.org/10.1145/3091528","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/7c229384-d41c-4195-92d6-1b5e24f18dd6","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/on-the-parameterized-complexity-of-finding-small-unsatisfiable-subsets-of-cnf-formulas-and-csp-instances(7c229384-d41c-4195-92d6-1b5e24f18dd6).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Computational Logic, 18(3):21. Association for Computing Machinery (ACM)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W30044362","https://openalex.org/W53965781","https://openalex.org/W119554023","https://openalex.org/W157230443","https://openalex.org/W178389848","https://openalex.org/W200564616","https://openalex.org/W285322218","https://openalex.org/W651308706","https://openalex.org/W986923873","https://openalex.org/W987035227","https://openalex.org/W1487965496","https://openalex.org/W1517036688","https://openalex.org/W1527197079","https://openalex.org/W1528594376","https://openalex.org/W1538237753","https://openalex.org/W1562906735","https://openalex.org/W1564397736","https://openalex.org/W1570425181","https://openalex.org/W1593288312","https://openalex.org/W1600919542","https://openalex.org/W1775889152","https://openalex.org/W1819966380","https://openalex.org/W1879512746","https://openalex.org/W1898652832","https://openalex.org/W1957114827","https://openalex.org/W1970736012","https://openalex.org/W1983648207","https://openalex.org/W1994520092","https://openalex.org/W1995725694","https://openalex.org/W1996184580","https://openalex.org/W2007464118","https://openalex.org/W2007979101","https://openalex.org/W2009147258","https://openalex.org/W2011992362","https://openalex.org/W2015211698","https://openalex.org/W2019717026","https://openalex.org/W2020681752","https://openalex.org/W2022841964","https://openalex.org/W2023379267","https://openalex.org/W2043107521","https://openalex.org/W2048685245","https://openalex.org/W2051627428","https://openalex.org/W2058793155","https://openalex.org/W2058937868","https://openalex.org/W2061513598","https://openalex.org/W2065251436","https://openalex.org/W2100404896","https://openalex.org/W2112660220","https://openalex.org/W2116087731","https://openalex.org/W2119274015","https://openalex.org/W2130190334","https://openalex.org/W2166566648","https://openalex.org/W2171456022","https://openalex.org/W2172085375","https://openalex.org/W2241862190","https://openalex.org/W2346933546","https://openalex.org/W2394717198","https://openalex.org/W2395574141","https://openalex.org/W2396459171","https://openalex.org/W2608239929","https://openalex.org/W2913688336","https://openalex.org/W2914414140","https://openalex.org/W2914965419","https://openalex.org/W2999916861","https://openalex.org/W3005406813","https://openalex.org/W3099451540","https://openalex.org/W4292230561"],"related_works":["https://openalex.org/W2796388654","https://openalex.org/W2036901448","https://openalex.org/W1656268799","https://openalex.org/W3107131366","https://openalex.org/W2038777323","https://openalex.org/W2558119813","https://openalex.org/W1608133301","https://openalex.org/W4283643926","https://openalex.org/W2168910274","https://openalex.org/W4385668771"],"abstract_inverted_index":{"In":[0,72,248],"many":[1],"practical":[2],"settings":[3],"it":[4,89],"is":[5,45,76,160,212,218,295,350],"useful":[6],"to":[7,92,151,162,297,310,321,340,370],"find":[8],"a":[9,14,25,49,54,129,183,241,266,336,346,356],"small":[10,198,242,332,357],"unsatisfiable":[11,16,34,199,243,333],"subset":[12,35,244,358],"of":[13,18,32,43,51,66,83,125,157,164,196,228,231,240,255,263,275,286,305,330,335,338,343,359],"given":[15,48,347],"set":[17,42,50,337],"constraints.":[19,360],"We":[20,95,187,214],"study":[21],"this":[22,152,158,217],"problem":[23,75,87,195,211,329,342],"from":[24],"parameterized":[26,373],"complexity":[27,131,374],"perspective,":[28],"taking":[29],"the":[30,33,37,41,67,74,84,106,115,178,191,194,210,220,226,229,260,273,280,284,293,303,312,314,317,328,341,364,367,378],"size":[31,319],"as":[36,63,177],"natural":[38],"parameter":[39],"where":[40,101],"constraints":[44,339],"either":[46],"(i)":[47],"clauses,":[52],"i.e.,":[53],"formula":[55],"in":[56,78,118,245],"conjunctive":[57],"normal":[58],"Form":[59],"(CNF),":[60],"or":[61,352],"(ii)":[62],"an":[64,81,238],"instance":[65,82],"Constraint":[68],"Satisfaction":[69],"Problem":[70],"(CSP).":[71],"general,":[73],"fixed-parameter":[77,111,202,299,323],"tractable.":[79],"For":[80,283],"propositional":[85],"satisfiability":[86,185],"(SAT),":[88],"was":[90],"known":[91],"be":[93],"W[1]-complete.":[94],"establish":[96,322,371],"A[2]-completeness":[97],"for":[98,105,114,190,204,208,222,237,302,377],"CSP":[99,139,192,306],"instances,":[100,307],"A[2]-hardness":[102],"prevails":[103],"already":[104,354],"Boolean":[107,138,170],"case.":[108],"With":[109],"these":[110],"intractability":[112],"results":[113,375],"general":[116],"case":[117,221,285,304],"mind,":[119],"we":[120,146,250,289,326,362],"consider":[121,251],"various":[122,252],"restricted":[123,253],"classes":[124,163,254],"inputs":[126,165,256],"and":[127,140,277,316],"draw":[128],"detailed":[130],"landscape.":[132],"It":[133],"turns":[134],"out":[135],"that":[136,166,173,189,216,265,291],"often":[137],"CNF":[141,223,287],"formulas":[142,224],"behave":[143],"similarly,":[144],"but":[145],"also":[147,219,376],"identify":[148],"notable":[149],"exceptions":[150],"rule.":[153],"The":[154],"main":[155],"part":[156],"article":[159],"dedicated":[161],"are":[167],"induced":[168],"by":[169,355],"constraint":[171,180],"languages":[172,181,207],"Schaefer":[174,206],"[1978]":[175],"identified":[176],"maximal":[179],"with":[182,225,257],"tractable":[184],"problem.":[186,380],"show":[188,215,290],"setting,":[193],"finding":[197,331],"subsets":[200,334],"remains":[201],"intractable":[203],"all":[205],"which":[209,235],"non-trivial.":[213],"exception":[227],"class":[230],"bijunctive":[232],"(Krom)":[233],"formulas,":[234,288],"allows":[236],"identification":[239],"polynomial":[246],"time.":[247],"addition,":[249],"bounds":[258,271,278],"on":[259,272,279],"maximum":[261],"number":[262],"times":[264],"variable":[267],"occurs":[268],"(the":[269],"degree),":[270],"arity":[274],"constraints,":[276],"domain":[281,318],"size.":[282],"restricting":[292],"degree":[294],"enough":[296],"obtain":[298],"tractability,":[300],"whereas":[301],"one":[308],"needs":[309],"restrict":[311],"degree,":[313],"arity,":[315],"simultaneously":[320],"tractability.":[324],"Finally,":[325],"relate":[327],"identifying":[344],"whether":[345],"variable-value":[348],"assignment":[349],"entailed":[351],"forbidden":[353],"Moreover,":[361],"use":[363],"connection":[365],"between":[366],"two":[368],"problems":[369],"similar":[372],"latter":[379]},"counts_by_year":[],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}