{"id":"https://openalex.org/W7140217806","doi":"https://doi.org/10.1109/tkde.2026.3677004","title":"A Fast Approximation Algorithm for the Top-$K$K Group Betweenness Centrality","display_name":"A Fast Approximation Algorithm for the Top-$K$K Group Betweenness Centrality","publication_year":2026,"publication_date":"2026-03-24","ids":{"openalex":"https://openalex.org/W7140217806","doi":"https://doi.org/10.1109/tkde.2026.3677004"},"language":null,"primary_location":{"id":"doi:10.1109/tkde.2026.3677004","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2026.3677004","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","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":null,"display_name":"Wenzheng Xu","orcid":"https://orcid.org/0000-0002-8396-6825"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenzheng Xu","raw_affiliation_strings":["College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-8396-6825","affiliations":[{"raw_affiliation_string":"College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jing Li","orcid":"https://orcid.org/0000-0002-7027-5574"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jing Li","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, Hong Kong, SAR China"],"raw_orcid":"https://orcid.org/0000-0002-7027-5574","affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Hong Kong, SAR China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Weifa Liang","orcid":"https://orcid.org/0000-0002-8207-6740"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Weifa Liang","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, Hong Kong, SAR China"],"raw_orcid":"https://orcid.org/0000-0002-8207-6740","affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Hong Kong, SAR China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zichuan Xu","orcid":"https://orcid.org/0000-0001-5438-1468"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zichuan Xu","raw_affiliation_strings":["School of Software, Dalian University of Technology, Dalian, China"],"raw_orcid":"https://orcid.org/0000-0001-5438-1468","affiliations":[{"raw_affiliation_string":"School of Software, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jian Peng","orcid":"https://orcid.org/0000-0001-5831-2240"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Peng","raw_affiliation_strings":["College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0001-5831-2240","affiliations":[{"raw_affiliation_string":"College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Pan Zhou","orcid":"https://orcid.org/0000-0002-8629-4622"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pan Zhou","raw_affiliation_strings":["School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-8629-4622","affiliations":[{"raw_affiliation_string":"School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Cheng Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128260","display_name":"Tianjin Energy Investment Group (China)","ror":"https://ror.org/03hmm9666","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210128260"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cheng Zhao","raw_affiliation_strings":["Sichuan Province Commercial Investment Group Company, Ltd., Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sichuan Province Commercial Investment Group Company, Ltd., Chengdu, China","institution_ids":["https://openalex.org/I4210128260"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Binyu Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binyu Yan","raw_affiliation_strings":["College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xiaohua Jia","orcid":"https://orcid.org/0000-0001-8702-8302"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiaohua Jia","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, Hong Kong, SAR China"],"raw_orcid":"https://orcid.org/0000-0001-8702-8302","affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Hong Kong, SAR China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jeffrey Xu Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jeffrey Xu Yu","raw_affiliation_strings":["Data Science and Analytics Thrust, The Hong Kong University of Science and Technology, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Science and Analytics Thrust, The Hong Kong University of Science and Technology, Guangzhou, China","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35805286,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"6","first_page":"3335","last_page":"3348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.946399986743927,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.946399986743927,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.028999999165534973,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.0044999998062849045,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/betweenness-centrality","display_name":"Betweenness centrality","score":0.902899980545044},{"id":"https://openalex.org/keywords/centrality","display_name":"Centrality","score":0.8931999802589417},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4260999858379364},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.41780000925064087},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.40400001406669617},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.39629998803138733}],"concepts":[{"id":"https://openalex.org/C117045392","wikidata":"https://www.wikidata.org/wiki/Q4899215","display_name":"Betweenness centrality","level":3,"score":0.902899980545044},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.8931999802589417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5940999984741211},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5006999969482422},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4260999858379364},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.40400001406669617},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38960000872612},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C137753397","wikidata":"https://www.wikidata.org/wiki/Q2434424","display_name":"Network science","level":3,"score":0.29600000381469727},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2630999982357025},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tkde.2026.3677004","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2026.3677004","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6916007399559021,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G235913322","display_name":null,"funder_award_id":"62272328","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W122652761","https://openalex.org/W1680189815","https://openalex.org/W1873406145","https://openalex.org/W1971421925","https://openalex.org/W1971937094","https://openalex.org/W2002240881","https://openalex.org/W2003408562","https://openalex.org/W2024982571","https://openalex.org/W2055438560","https://openalex.org/W2095293504","https://openalex.org/W2112556110","https://openalex.org/W2152255412","https://openalex.org/W2171707538","https://openalex.org/W2344526012","https://openalex.org/W2368841069","https://openalex.org/W2388242991","https://openalex.org/W2574529824","https://openalex.org/W2614250740","https://openalex.org/W2616591171","https://openalex.org/W2790166049","https://openalex.org/W2884593183","https://openalex.org/W2912469236","https://openalex.org/W2963501991","https://openalex.org/W3032945343","https://openalex.org/W3158360526","https://openalex.org/W3160322580","https://openalex.org/W3171018669","https://openalex.org/W3185638932","https://openalex.org/W4225299183","https://openalex.org/W4235019172","https://openalex.org/W4312037431","https://openalex.org/W4379924867","https://openalex.org/W4385270233","https://openalex.org/W4413349707"],"related_works":[],"abstract_inverted_index":{"Betweenness":[0],"centrality":[1,7,33,85,140,153,218],"is":[2,35,60,92,121,154,207,226],"one":[3],"of":[4,40,51,82,86,118,141,200,219],"the":[5,48,57,69,74,79,83,116,139,147,152,158,174,198,204,214,217,220,224,233],"key":[6],"measures":[8],"in":[9,15,20,25,126],"many":[10,113],"applications":[11],"including":[12],"community":[13],"detections":[14,19],"biological":[16],"networks,":[17,22,27],"vulnerability":[18],"communication":[21],"misinformation":[23],"filtering":[24],"social":[26],"etc.":[28],"The":[29],"top-K":[30],"group":[31,39,88,144,187,221],"betweenness":[32],"problem":[34],"to":[36,137,163,209],"find":[37,164,184],"a":[38,44,96,132,142,165,185],"K":[41,58,108],"nodes":[42,59],"from":[43,89],"network":[45],"so":[46],"that":[47,54,73,135,197],"total":[49],"fraction":[50],"shortest":[52],"paths":[53],"pass":[55],"through":[56],"maximized.":[61],"Existing":[62],"studies":[63,76],"proposed":[64,175,205],"randomized":[65],"sampling":[66],"algorithms":[67],"for":[68,100],"problem.":[70],"We":[71,168],"notice":[72],"existing":[75],"ensured":[77],"that,":[78,172],"maximum":[80],"deviation":[81],"estimated":[84],"every":[87],"its":[90],"expectation":[91],"no":[93,105,227],"greater":[94],"than":[95,107,213,229,232],"small":[97],"given":[98],"threshold":[99],"all":[101],"potential":[102],"groups":[103,120],"with":[104,188,193],"more":[106,161,228],"nodes,":[109],"thereby":[110],"generating":[111],"too":[112],"samples,":[114,180],"as":[115],"number":[117,199],"such":[119],"prohibitively":[122],"large.":[123],"In":[124],"contrast,":[125],"this":[127],"paper":[128],"we":[129],"first":[130],"devise":[131],"novel":[133],"algorithm":[134,148,159,176,206,225],"enables":[136],"estimate":[138],"tentative":[143],"adaptively,":[145],"and":[146],"immediately":[149],"stops":[150],"once":[151],"large":[155],"enough;":[156],"otherwise,":[157],"uses":[160,177],"samples":[162,201],"better":[166],"group.":[167],"then":[169],"theoretically":[170],"show":[171],"even":[173],"much":[178],"less":[179],"it":[181],"still":[182],"can":[183],"performance-guaranteed":[186],"high":[189],"probability.":[190],"Experimental":[191],"results":[192],"real-world":[194],"networks":[195],"demonstrate":[196],"used":[202],"by":[203,223],"up":[208],"36":[210],"times":[211],"smaller":[212,231],"state-of-the-art,":[215],"while":[216],"found":[222],"4.5%":[230],"latter.":[234]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-03-25T00:00:00"}