{"id":"https://openalex.org/W1906408003","doi":"https://doi.org/10.1145/2736696","title":"A SAT Approach to Clique-Width","display_name":"A SAT Approach to Clique-Width","publication_year":2015,"publication_date":"2015-06-02","ids":{"openalex":"https://openalex.org/W1906408003","doi":"https://doi.org/10.1145/2736696","mag":"1906408003"},"language":"en","primary_location":{"id":"doi:10.1145/2736696","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2736696","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/A5025921874","display_name":"Marijn J. H. Heule","orcid":"https://orcid.org/0000-0002-5587-8801"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marijn J. H. Heule","raw_affiliation_strings":["Department of Computer Sciences, The University of Texas at Austin, Austin, Texas, United States"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, The University of Texas at Austin, Austin, Texas, United States","institution_ids":["https://openalex.org/I86519309"]}]},{"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":["Institute of Computer Graphics and Algorithms, TU Wien, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Graphics and Algorithms, TU Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025921874"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":3.2746,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.92143081,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"3","first_page":"1","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983000159263611,"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":0.9983000159263611,"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/T11567","display_name":"semigroups and automata theory","score":0.9951000213623047,"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/T10142","display_name":"Formal Methods in Verification","score":0.9944000244140625,"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/clique-problem","display_name":"Clique problem","score":0.6688893437385559},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6226845383644104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6127784252166748},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.5696855187416077},{"id":"https://openalex.org/keywords/clique-graph","display_name":"Clique graph","score":0.5315352082252502},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.49806928634643555},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.4674326777458191},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.44995951652526855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44891035556793213},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.42543643712997437},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3527984023094177},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.31931495666503906},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.2522366940975189},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19662967324256897},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.15488436818122864},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.11651793122291565},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.06943649053573608}],"concepts":[{"id":"https://openalex.org/C150997102","wikidata":"https://www.wikidata.org/wiki/Q1196873","display_name":"Clique problem","level":5,"score":0.6688893437385559},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6226845383644104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6127784252166748},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.5696855187416077},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.5315352082252502},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.49806928634643555},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.4674326777458191},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.44995951652526855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44891035556793213},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.42543643712997437},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3527984023094177},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.31931495666503906},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.2522366940975189},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19662967324256897},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.15488436818122864},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.11651793122291565},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.06943649053573608},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2736696","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2736696","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:CiteSeerX.psu:10.1.1.706.1747","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.706.1747","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.utexas.edu/%7Emarijn/publications/cwd-tocl-final.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.771.6482","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.771.6482","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/1304.5498.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1002097251","display_name":null,"funder_award_id":"239962","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G1328205237","display_name":null,"funder_award_id":"CNS-0910913","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8402539981","display_name":null,"funder_award_id":"N66001-10-2-4087","funder_id":"https://openalex.org/F4320337531","funder_display_name":"Defense Sciences Office, DARPA"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320337531","display_name":"Defense Sciences Office, DARPA","ror":"https://ror.org/0447fe631"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W51566375","https://openalex.org/W77305285","https://openalex.org/W78552530","https://openalex.org/W96963885","https://openalex.org/W1511963917","https://openalex.org/W1513230022","https://openalex.org/W1518705996","https://openalex.org/W1549449731","https://openalex.org/W1550483759","https://openalex.org/W1560032421","https://openalex.org/W1628915153","https://openalex.org/W1821762897","https://openalex.org/W1835083164","https://openalex.org/W1864537025","https://openalex.org/W1878922758","https://openalex.org/W1976120600","https://openalex.org/W1990600049","https://openalex.org/W1993328543","https://openalex.org/W1994887153","https://openalex.org/W1999396796","https://openalex.org/W2015142920","https://openalex.org/W2019030165","https://openalex.org/W2025013668","https://openalex.org/W2035344492","https://openalex.org/W2053991811","https://openalex.org/W2060493079","https://openalex.org/W2062170486","https://openalex.org/W2063132075","https://openalex.org/W2063951771","https://openalex.org/W2067475075","https://openalex.org/W2070374625","https://openalex.org/W2087911394","https://openalex.org/W2096112628","https://openalex.org/W2100609826","https://openalex.org/W2109716789","https://openalex.org/W2118406528","https://openalex.org/W2121341976","https://openalex.org/W2128021849","https://openalex.org/W2137616550","https://openalex.org/W2154682992","https://openalex.org/W2170923601","https://openalex.org/W2171507355","https://openalex.org/W2174973502","https://openalex.org/W2299079197","https://openalex.org/W2605289564","https://openalex.org/W2778763315","https://openalex.org/W3121193618"],"related_works":["https://openalex.org/W1991604152","https://openalex.org/W4315881088","https://openalex.org/W2231732554","https://openalex.org/W2936075899","https://openalex.org/W2079220110","https://openalex.org/W2963574048","https://openalex.org/W2186006531","https://openalex.org/W2002621149","https://openalex.org/W4318426939","https://openalex.org/W3003390052"],"abstract_inverted_index":{"Clique-width":[0],"is":[1,21,29,53,62,84],"a":[2,19,39,57,65,121,141],"graph":[3,20],"invariant":[4],"that":[5,73,119,145],"has":[6,146],"been":[7],"widely":[8],"studied":[9],"in":[10,69],"combinatorics":[11],"and":[12,164],"computational":[13],"logic.":[14],"Computing":[15],"the":[16,26,85,89,101,116,136,162],"clique-width":[17,28,44,68,91,138,144,163,166],"of":[18,67,71,78,92,108,139,143,167],"an":[22,46,75,152],"intricate":[23],"problem,":[24],"because":[25],"exact":[27,90],"not":[30],"known":[31],"even":[32],"for":[33,42,157,161],"very":[34],"small":[35,94,122],"graphs.":[36,170],"We":[37,125],"present":[38],"new":[40],"method":[41,83,130],"computing":[43],"via":[45],"encoding":[47,61,77],"to":[48,87,134],"propositional":[49],"satisfiability":[50],"(SAT),":[51],"which":[52],"then":[54],"evaluated":[55],"by":[56],"SAT":[58],"solver.":[59],"Our":[60,81],"based":[63],"on":[64],"reformulation":[66],"terms":[70],"partitions":[72],"utilizes":[74],"efficient":[76],"cardinality":[79],"constraints.":[80],"SAT-based":[82],"first":[86],"discover":[88],"various":[93,109],"graphs,":[95,140],"including":[96],"famous":[97,168],"named":[98,169],"graphs":[99,107,118],"from":[100],"literature":[102],"as":[103,105],"well":[104],"random":[106],"density.":[110],"With":[111],"our":[112,129],"method,":[113],"we":[114,154],"determined":[115],"smallest":[117],"require":[120],"predescribed":[123],"clique-width.":[124],"further":[126],"show":[127],"how":[128],"can":[131],"be":[132],"modified":[133],"compute":[135],"linear":[137,165],"variant":[142],"recently":[147],"received":[148],"considerable":[149],"attention.":[150],"In":[151],"appendix,":[153],"provide":[155],"certificates":[156],"tight":[158],"upper":[159],"bounds":[160]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
