{"id":"https://openalex.org/W1996791172","doi":"https://doi.org/10.1137/09076619x","title":"Finding, Minimizing, and Counting Weighted Subgraphs","display_name":"Finding, Minimizing, and Counting Weighted Subgraphs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1996791172","doi":"https://doi.org/10.1137/09076619x","mag":"1996791172"},"language":"en","primary_location":{"id":"doi:10.1137/09076619x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09076619x","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":["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/A5044244682","display_name":"Virginia Vassilevska Williams","orcid":"https://orcid.org/0000-0003-4844-2863"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Virginia Vassilevska Williams","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063871533","display_name":"Ryan Williams","orcid":"https://orcid.org/0000-0003-2326-2233"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ryan Williams","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044244682"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6133,"has_fulltext":false,"cited_by_count":83,"citation_normalized_percentile":{"value":0.97660741,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"42","issue":"3","first_page":"831","last_page":"854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T12541","display_name":"Graph Labeling and Dimension Problems","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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7902392148971558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.659101128578186},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5706517100334167},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5144929885864258},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5055580139160156},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4918825626373291},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.46957892179489136},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4276581406593323}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7902392148971558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.659101128578186},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5706517100334167},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5144929885864258},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5055580139160156},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4918825626373291},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.46957892179489136},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4276581406593323},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/09076619x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09076619x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1967066104","https://openalex.org/W1977699786","https://openalex.org/W1979740015","https://openalex.org/W1991858502","https://openalex.org/W2012473793","https://openalex.org/W2023600080","https://openalex.org/W2049253486","https://openalex.org/W2049647076","https://openalex.org/W2055245094","https://openalex.org/W2072985157","https://openalex.org/W2084732238","https://openalex.org/W2089633648","https://openalex.org/W2102039892","https://openalex.org/W2137874581","https://openalex.org/W2150875823","https://openalex.org/W2153622112","https://openalex.org/W2153624566","https://openalex.org/W2296148711","https://openalex.org/W2313391498","https://openalex.org/W4213071546","https://openalex.org/W4234675635","https://openalex.org/W4246456962"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W4205377127","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W3106434744"],"abstract_inverted_index":{"For":[0],"a":[1,26,106,173,206],"pattern":[2],"graph":[3,29],"$H$":[4,24,59,122],"on":[5,31,132,238],"$k$":[6,153],"nodes,":[7,33],"we":[8,97],"consider":[9],"the":[10,16,50,103,148,167,185,235,252],"problems":[11],"of":[12,18,23,55,57,64,105,118,120,164,169,187,193,210,219],"finding":[13,37],"and":[14,44,75,84,113,152,189,204],"counting":[15],"number":[17,54,117,168],"(not":[19],"necessarily":[20],"induced)":[21],"copies":[22,40,56,119,170],"in":[25,41,71,80,137,223,244],"given":[27],"large":[28],"$G$":[30],"$n$":[32],"as":[34,36],"well":[35],"minimum":[38,124],"weight":[39,175,220],"both":[42],"node-weighted":[43,260],"edge-weighted":[45,217,253],"graphs.":[46],"Our":[47],"results":[48,159],"include":[49],"following:":[51],"1.":[52],"The":[53,116],"an":[58,61,216],"with":[60],"independent":[62],"set":[63],"size":[65],"$s$":[66],"can":[67,134,176,241],"be":[68,135,177,242],"computed":[69],"exactly":[70,172,221],"$O^*(2^s":[72],"n^{k-s+3})$":[73,82],"time":[74,83,228],"$poly(n,k)+O(2^s":[76],"n^2)$":[77],"space,":[78],"or":[79],"$O^*(4^s":[81],"$poly(n,k)$":[85],"space.":[86],"(The":[87],"$O^*$":[88],"notation":[89],"omits":[90],"$poly(k)$":[91],"factors.)":[92],"To":[93],"obtain":[94],"these":[95],"algorithms":[96,100,183],"provide":[98],"fast":[99],"for":[101,161,229],"computing":[102],"permanent":[104],"$k":[107],"\\times":[108],"n$":[109],"matrix":[110,149],"over":[111],"rings":[112],"semirings.":[114],"2.":[115],"any":[121],"having":[123,171],"(or":[125],"maximum)":[126],"node-weight":[127],"(with":[128],"arbitrary":[129],"real":[130],"weights":[131],"nodes)":[133],"found":[136,178],"$O(n^{\\omega":[138],"k/3}":[139],"+":[140],"n^{2k/3+o(1)})$":[141],"time,":[142],"where":[143],"$\\omega":[144],"<":[145],"2.38$":[146],"is":[147,154,255],"multiplication":[150],"exponent":[151],"divisible":[155],"by":[156],"$3$.":[157],"Similar":[158],"hold":[160],"other":[162],"values":[163],"$k$.":[165],"Also,":[166],"prescribed":[174],"within":[179],"this":[180],"time.":[181,248],"These":[182],"extend":[184],"technique":[186],"Czumaj":[188],"Lingas":[190],"[in":[191],"Proceedings":[192],"SODA":[194],"2007,":[195,201],"ACM,":[196],"New":[197],"York,":[198],"SIAM,":[199],"Philadelphia,":[200],"pp.":[202],"986--994]":[203],"give":[205],"new":[207],"(algorithmic)":[208],"application":[209],"multiparty":[211],"communication":[212],"complexity.":[213],"3.":[214],"Finding":[215],"triangle":[218],"$0$":[222],"general":[224],"graphs":[225],"requires":[226],"$\\Omega(n^{3-\\varepsilon})$":[227],"all":[230],"$\\varepsilon":[231],">":[232],"0$,":[233],"unless":[234],"$3$SUM":[236],"problem":[237,254],"$N$":[239],"numbers":[240],"solved":[243],"$O(N^{2":[245],"-":[246],"\\varepsilon})$":[247],"This":[249],"suggests":[250],"that":[251],"much":[256],"harder":[257],"than":[258],"its":[259],"version.":[261]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}