{"id":"https://openalex.org/W1508908353","doi":"https://doi.org/10.1137/130947076","title":"Known Algorithms for Edge Clique Cover are Probably Optimal","display_name":"Known Algorithms for Edge Clique Cover are Probably Optimal","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1508908353","doi":"https://doi.org/10.1137/130947076","mag":"1508908353"},"language":"en","primary_location":{"id":"doi:10.1137/130947076","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130947076","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/1203.1754","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037989463","display_name":"Marek Cygan","orcid":"https://orcid.org/0000-0003-2472-2975"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marek Cygan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059330513","display_name":"Marcin Pilipczuk","orcid":"https://orcid.org/0000-0001-5680-7397"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcin Pilipczuk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000479623","display_name":"Micha\u0142 Pilipczuk","orcid":"https://orcid.org/0000-0001-7891-1988"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00308298,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"45","issue":"1","first_page":"67","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991999864578247,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991999864578247,"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":0.9980000257492065,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.8158342242240906},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7457124590873718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6276155710220337},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.6104496121406555},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5781269669532776},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5515058040618896},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.5509341359138489},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5494715571403503},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5051549077033997},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4830920696258545},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4588104486465454},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4273393154144287},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4252665042877197},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4178640842437744},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4106302559375763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17243897914886475}],"concepts":[{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.8158342242240906},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7457124590873718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6276155710220337},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6104496121406555},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5781269669532776},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5515058040618896},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.5509341359138489},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5494715571403503},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5051549077033997},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4830920696258545},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4588104486465454},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4273393154144287},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4252665042877197},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4178640842437744},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4106302559375763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17243897914886475},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130947076","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130947076","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1203.1754","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.1754","pdf_url":"https://arxiv.org/pdf/1203.1754","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":"","raw_type":"text"},{"id":"mag:1508908353","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1203.1754","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1203.1754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1203.1754","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1203.1754","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.1754","pdf_url":"https://arxiv.org/pdf/1203.1754","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1508908353.pdf","grobid_xml":"https://content.openalex.org/works/W1508908353.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W33845589","https://openalex.org/W1567268701","https://openalex.org/W1579811457","https://openalex.org/W1676006881","https://openalex.org/W1775843101","https://openalex.org/W1787126581","https://openalex.org/W1968481794","https://openalex.org/W1971799322","https://openalex.org/W1981296715","https://openalex.org/W1982442837","https://openalex.org/W1985572324","https://openalex.org/W1987263710","https://openalex.org/W1992349235","https://openalex.org/W1995725694","https://openalex.org/W1998964055","https://openalex.org/W1999145171","https://openalex.org/W2006048213","https://openalex.org/W2009147258","https://openalex.org/W2011039300","https://openalex.org/W2023652218","https://openalex.org/W2023839655","https://openalex.org/W2034437384","https://openalex.org/W2038636594","https://openalex.org/W2040081895","https://openalex.org/W2041837101","https://openalex.org/W2051784313","https://openalex.org/W2058258808","https://openalex.org/W2059453880","https://openalex.org/W2064280346","https://openalex.org/W2087638517","https://openalex.org/W2107284348","https://openalex.org/W2116453796","https://openalex.org/W2130190334","https://openalex.org/W2137560895","https://openalex.org/W2139087151","https://openalex.org/W2140408741","https://openalex.org/W2145152745","https://openalex.org/W2147507978","https://openalex.org/W2150004999","https://openalex.org/W2162561603","https://openalex.org/W2321467776","https://openalex.org/W2568150489","https://openalex.org/W2610196513","https://openalex.org/W2950987206"],"related_works":["https://openalex.org/W2405999865","https://openalex.org/W2134469776","https://openalex.org/W2604969355","https://openalex.org/W2794380282","https://openalex.org/W2775084241","https://openalex.org/W65530203","https://openalex.org/W1558321388","https://openalex.org/W3088630545","https://openalex.org/W2977999826","https://openalex.org/W3160700943","https://openalex.org/W2626384263","https://openalex.org/W3038344752","https://openalex.org/W2963439929","https://openalex.org/W2962811261","https://openalex.org/W2539516785","https://openalex.org/W2949062889","https://openalex.org/W3158696645","https://openalex.org/W2951838648","https://openalex.org/W2950485803","https://openalex.org/W2185076815"],"abstract_inverted_index":{"In":[0,109],"the":[1,39,60,70,73,85,115,168,172,189],"Edge":[2],"Clique":[3],"Cover":[4],"(ECC)":[5],"problem,":[6,170],"given":[7],"an":[8,13,131,143],"undirected":[9],"graph":[10],"$G$":[11,25,31,65],"and":[12,139,153],"integer":[14],"$k$,":[15],"we":[16,112,124],"ask":[17],"whether":[18],"one":[19,37],"can":[20],"choose":[21],"$k$":[22],"cliques":[23],"in":[24,34],"such":[26],"that":[27,58,77,114,129],"each":[28],"edge":[29],"of":[30,38,55,62,64,117,134,201],"is":[32,94,121,161],"contained":[33],"at":[35,75,88],"least":[36],"chosen":[40],"cliques.":[41],"Gramm":[42,118],"et":[43,119],"al.":[44,120],"[ACM":[45],"J.":[46],"Exp.":[47],"Algorithmics,":[48],"13":[49],"(2008)]":[50],"have":[51,80],"shown":[52,81],"a":[53,82,103,126,195,199],"set":[54],"simple":[56],"rules":[57],"reduce":[59],"number":[61],"vertices":[63],"to":[66,72,142],"$2^k$":[67,90],"while":[68],"preserving":[69],"answer":[71],"instance":[74,133,146],"hand,":[76],"is,":[78],"they":[79],"kernel":[83,200],"for":[84,167],"problem":[86,191],"with":[87,96,136,148],"most":[89],"vertices.":[91],"No":[92],"algorithm":[93,128,166],"known":[95],"significantly":[97],"better":[98],"running":[99],"time":[100,165],"bound":[101],"than":[102],"brute-force":[104],"search":[105],"on":[106],"this":[107,110],"kernel.":[108],"paper,":[111],"show":[113],"approach":[116],"essentially":[122],"optimal:":[123],"present":[125],"polynomial-time":[127],"reduces":[130],"arbitrary":[132],"$3$-CNF-SAT":[135],"$n$":[137],"variables":[138],"$m$":[140],"clauses":[141],"equivalent":[144],"ECC":[145,169,190],"$(G,k)$":[147],"$k":[149],"=":[150,155,186],"\\mathcal{O}(\\log":[151],"n)$":[152],"$|V(G)|":[154],"\\mathcal{O}(n":[156],"+":[157],"m)$.":[158],"Consequently,":[159],"there":[160],"no":[162],"$2^{2^{o(k)}}{\\rm":[163],"poly}(n)$":[164],"unless":[171,183],"Exponential":[173],"Time":[174],"Hypothesis":[175],"fails.":[176],"Moreover,":[177],"our":[178],"reduction":[179],"also":[180],"implies":[181],"that,":[182],"P":[184],"$":[185,187],"NP,":[188],"does":[192],"not":[193],"admit":[194],"subexponential":[196],"kernel,":[197],"i.e.,":[198],"size":[202],"$2^{o(k)}$.":[203]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
