{"id":"https://openalex.org/W3193379831","doi":"https://doi.org/10.1109/access.2021.3106266","title":"buTCS: An Optimized Algorithm for Estimating the Size of Transitive Closure","display_name":"buTCS: An Optimized Algorithm for Estimating the Size of Transitive Closure","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3193379831","doi":"https://doi.org/10.1109/access.2021.3106266","mag":"3193379831"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3106266","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3106266","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09519716.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09519716.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101647642","display_name":"Xiaozhe Li","orcid":"https://orcid.org/0000-0003-0035-2287"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaozhe Li","raw_affiliation_strings":["School of Computer Science and Technology, Donghua University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-0035-2287","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Donghua University, Shanghai, China","institution_ids":["https://openalex.org/I181326427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100329016","display_name":"Xuan Wang","orcid":"https://orcid.org/0000-0002-7586-5741"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Wang","raw_affiliation_strings":["School of Computer Science and Technology, Donghua University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-7586-5741","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Donghua University, Shanghai, China","institution_ids":["https://openalex.org/I181326427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055891868","display_name":"Junfeng Zhou","orcid":"https://orcid.org/0000-0001-6494-5319"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junfeng Zhou","raw_affiliation_strings":["School of Computer Science and Technology, Donghua University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0001-6494-5319","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Donghua University, Shanghai, China","institution_ids":["https://openalex.org/I181326427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035378893","display_name":"Ming Du","orcid":"https://orcid.org/0000-0002-8617-8939"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming Du","raw_affiliation_strings":["School of Computer Science and Technology, Donghua University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-8617-8939","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Donghua University, Shanghai, China","institution_ids":["https://openalex.org/I181326427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I181326427"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.14155775,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"9","issue":null,"first_page":"116528","last_page":"116539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9932000041007996,"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/T11106","display_name":"Data Management and Algorithms","score":0.9724000096321106,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9660000205039978,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transitive-closure","display_name":"Transitive closure","score":0.8851331472396851},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5845787525177002},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5819976329803467},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5625832080841064},{"id":"https://openalex.org/keywords/transitive-reduction","display_name":"Transitive reduction","score":0.47289884090423584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.314700722694397},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.1707909107208252},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1532592475414276},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.06393113732337952}],"concepts":[{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.8851331472396851},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5845787525177002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5819976329803467},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5625832080841064},{"id":"https://openalex.org/C129691609","wikidata":"https://www.wikidata.org/wiki/Q3088151","display_name":"Transitive reduction","level":5,"score":0.47289884090423584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.314700722694397},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.1707909107208252},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1532592475414276},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.06393113732337952},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2021.3106266","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3106266","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09519716.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:2a497d94c2354b3d97e0e04a587b5008","is_oa":true,"landing_page_url":"https://doaj.org/article/2a497d94c2354b3d97e0e04a587b5008","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 9, Pp 116528-116539 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3106266","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3106266","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09519716.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1929525032","display_name":null,"funder_award_id":"61472339","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2384550236","display_name":"\u5927\u89c4\u6a21\u52a8\u6001\u6570\u636e\u56fe\u4e0a\u7684\u591a\u7ea6\u675f\u53ef\u8fbe\u67e5\u8be2\u5904\u7406\u6280\u672f","funder_award_id":"20ZR1402700","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G4017787111","display_name":null,"funder_award_id":"61572421","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G634456673","display_name":"\u9762\u5411XML\u6570\u636e\u7684\u5173\u952e\u5b57\u67e5\u8be2\u7b97\u6cd5\u8f85\u52a9\u751f\u6210\u6280\u672f\u7814\u7a76","funder_award_id":"61272124","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6423249898","display_name":null,"funder_award_id":"61873337","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6607675504","display_name":null,"funder_award_id":"61472339, 61873337","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320309612","display_name":"Natural Science Foundation of Shanghai","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3193379831.pdf","grobid_xml":"https://content.openalex.org/works/W3193379831.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W40760629","https://openalex.org/W1501937057","https://openalex.org/W1979740015","https://openalex.org/W1987480024","https://openalex.org/W1997898455","https://openalex.org/W2017139167","https://openalex.org/W2020284609","https://openalex.org/W2026154596","https://openalex.org/W2030166143","https://openalex.org/W2034956447","https://openalex.org/W2045713925","https://openalex.org/W2053593718","https://openalex.org/W2061257729","https://openalex.org/W2090263269","https://openalex.org/W2110920860","https://openalex.org/W2127114148","https://openalex.org/W2131692673","https://openalex.org/W2155066775","https://openalex.org/W2155508779","https://openalex.org/W2613786374","https://openalex.org/W2752885492","https://openalex.org/W2758611777","https://openalex.org/W2790619200","https://openalex.org/W2795048224","https://openalex.org/W2970143390","https://openalex.org/W6601688091","https://openalex.org/W6664156239"],"related_works":["https://openalex.org/W2075704325","https://openalex.org/W1553139688","https://openalex.org/W1503149859","https://openalex.org/W2044040096","https://openalex.org/W2008080405","https://openalex.org/W4366828350","https://openalex.org/W2038086027","https://openalex.org/W2362009423","https://openalex.org/W2070329106","https://openalex.org/W2357069572"],"abstract_inverted_index":{"Given":[0],"a":[1,5,137,151],"directed":[2],"graph":[3],"and":[4,70,129,149],"node":[6],"<inline-formula":[7,23,35],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,19,24,36,47,61,77,92,114,140,174,181],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[9,25,37],"<tex-math":[10,26,38],"notation=\"LaTeX\">$v$":[11,27,39],"</tex-math></inline-formula>":[12,28,40],",":[13,116],"the":[14,30,44,57,83,90,161],"transitive":[15],"closure":[16],"(":[17],"<italic":[18,46,60,76,91,113,139,173,180],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">TC</i>":[20,48,62,78,93,141,182],")":[21],"of":[22,32,59,146],"is":[29,50,65,134],"set":[31],"nodes":[33],"that":[34,100,145,172],"can":[41],"reach":[42],"in":[43,53,67,126],"graph.":[45],"size":[49,63,79,94,142,183],"very":[51],"important":[52],"many":[54],"applications":[55],"but":[56],"cost":[58],"computation":[64],"high":[66],"both":[68],"time":[69,128],"space,":[71],"which":[72],"makes":[73],"computing":[74],"accurate":[75,121],"not":[80],"applicable":[81],"to":[82,88,117,135,159],"scenario":[84],"where":[85],"we":[86,108],"need":[87],"know":[89],"quickly":[95],"for":[96],"large":[97],"graphs.":[98],"Considering":[99],"existing":[101],"approaches":[102],"are":[103],"either":[104],"inefficient":[105],"or":[106],"inaccurate,":[107],"propose":[109,156],"an":[110],"algorithm,":[111],"namely":[112],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">buTCS</i>":[115,175],"efficiently":[118],"make":[119],"more":[120],"estimation.":[122],"Our":[123],"approach":[124],"works":[125],"linear":[127],"space.":[130],"The":[131,164],"basic":[132],"idea":[133],"compute":[136],"node\u2019s":[138],"based":[143],"on":[144,167,179],"its":[147],"out-neighbors":[148],"perform":[150],"top-down":[152],"verification.":[153],"We":[154],"further":[155],"two":[157],"optimizations":[158],"improve":[160],"estimation":[162,178],"accuracy.":[163],"experimental":[165],"results":[166],"13":[168],"real":[169],"datasets":[170],"show":[171],"achieves":[176],"better":[177],"efficiently.":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}