{"id":"https://openalex.org/W2768030941","doi":"https://doi.org/10.1137/15m1044874","title":"On Clustering Induced Voronoi Diagrams","display_name":"On Clustering Induced Voronoi Diagrams","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2768030941","doi":"https://doi.org/10.1137/15m1044874","mag":"2768030941"},"language":"en","primary_location":{"id":"doi:10.1137/15m1044874","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1044874","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/A5060901632","display_name":"Danny Z. Chen","orcid":"https://orcid.org/0000-0001-6565-2884"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Danny Z. Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037816092","display_name":"Ziyun Huang","orcid":"https://orcid.org/0000-0003-3484-7907"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ziyun Huang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000028651","display_name":"Yangwei Liu","orcid":"https://orcid.org/0000-0001-9653-5760"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yangwei Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006945148","display_name":"Jinhui Xu","orcid":"https://orcid.org/0000-0001-5730-9429"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinhui Xu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060901632"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5938,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7484304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"46","issue":"6","first_page":"1679","last_page":"1711"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9986000061035156,"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.9652441740036011},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6454918384552002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6082234382629395},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5767719745635986},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5742133855819702},{"id":"https://openalex.org/keywords/power-diagram","display_name":"Power diagram","score":0.5251904726028442},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4654676914215088},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4254317879676819},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4190070629119873},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.416255921125412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23624855279922485},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12245863676071167},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10100150108337402},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07114362716674805}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.9652441740036011},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6454918384552002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6082234382629395},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5767719745635986},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5742133855819702},{"id":"https://openalex.org/C20573064","wikidata":"https://www.wikidata.org/wiki/Q13410436","display_name":"Power diagram","level":3,"score":0.5251904726028442},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4654676914215088},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4254317879676819},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4190070629119873},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.416255921125412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23624855279922485},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12245863676071167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10100150108337402},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07114362716674805},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1044874","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1044874","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":[{"id":"https://openalex.org/G1039314466","display_name":null,"funder_award_id":"IIS-1115220","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1780730485","display_name":null,"funder_award_id":"CCF-1217906","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8087143962","display_name":null,"funder_award_id":"CCF-1422324","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8451944197","display_name":null,"funder_award_id":"IIS-1422591","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1967005434","https://openalex.org/W1970610912","https://openalex.org/W2015751084","https://openalex.org/W2021565542","https://openalex.org/W2048475323","https://openalex.org/W2054011861","https://openalex.org/W2059004575","https://openalex.org/W2073517977","https://openalex.org/W2079206375","https://openalex.org/W2079666190","https://openalex.org/W2100928221","https://openalex.org/W2126751256","https://openalex.org/W2140901978","https://openalex.org/W2160009442","https://openalex.org/W2427881153","https://openalex.org/W4206696315","https://openalex.org/W4234003491"],"related_works":["https://openalex.org/W2351580801","https://openalex.org/W2015548030","https://openalex.org/W1992160534","https://openalex.org/W2739428663","https://openalex.org/W2392199123","https://openalex.org/W2116864555","https://openalex.org/W2389383186","https://openalex.org/W2054912417","https://openalex.org/W2084447131","https://openalex.org/W1518796918"],"abstract_inverted_index":{"In":[0],"this":[1,207],"paper,":[2],"we":[3,146,209,235],"study":[4],"a":[5,87,123,131,149,176,201,215],"generalization":[6],"of":[7,33,38,44,59,89,122,134,180,203,250],"the":[8,13,21,29,54,70,75,99,111,115,120,159,168,172,195,222],"classical":[9],"Voronoi":[10,16,77,100],"diagram,":[11],"called":[12,153],"clustering":[14,94],"induced":[15],"diagram":[17,101],"(CIVD).":[18],"Different":[19],"from":[20,194],"traditional":[22],"model,":[23],"CIVD":[24,46,129,161,239,242],"takes":[25],"as":[26],"its":[27],"sites":[28],"power":[30],"set":[31,36,132],"$U$":[32],"an":[34,48,65],"input":[35],"$P$":[37,133],"objects.":[39],"For":[40],"each":[41,187,219],"subset":[42,202],"$C$":[43,63],"$P$,":[45],"uses":[47],"influence":[49,58,116,155,193],"function":[50,117],"$F(C,q)$":[51],"to":[52,98,213],"measure":[53],"total":[55],"(or":[56],"joint)":[57],"all":[60,184],"objects":[61],"in":[62,69,79,105,137,186,221,263],"on":[64,206],"arbitrary":[66],"point":[67],"$q$":[68],"space":[71,96,173],"$\\mathbb{R}^d$":[72,80,138],"and":[73,95,224,243,246,266],"determines":[74],"influence-based":[76],"cell":[78,188,220],"for":[81,114,130,139,158,218,229],"$C$.":[82],"This":[83],"generalized":[84],"model":[85],"offers":[86],"number":[88,179],"new":[90,107,151],"features":[91],"(e.g.,":[92,125],"simultaneous":[93],"partition)":[97],"which":[102,118],"are":[103],"useful":[104],"various":[106,226],"applications.":[108],"We":[109],"investigate":[110],"general":[112,160],"conditions":[113],"ensure":[119],"existence":[121],"small-size":[124],"nearly":[126,177],"linear)":[127],"approximate":[128,154,191],"$n$":[135],"points":[136,185],"some":[140,230],"fixed":[141,232],"$d$.":[142],"To":[143],"construct":[144],"CIVD,":[145,245],"first":[147],"present":[148],"stand-alone":[150],"technique,":[152,208],"(AI)":[156],"decomposition,":[157],"problem.":[162],"With":[163],"only":[164],"$O(n\\log":[165],"n)$":[166,269],"time,":[167,270],"AI":[169],"decomposition":[170,223],"partitions":[171],"$\\mathbb{R}^{d}$":[174],"into":[175],"linear":[178],"cells":[181],"so":[182],"that":[183,248],"receive":[189],"their":[190,257],"maximum":[192],"same":[196],"(possibly":[197],"unknown)":[198],"site":[199,217],"(i.e.,":[200],"$P$).":[204],"Based":[205],"develop":[210],"assignment":[211,254],"algorithms":[212],"determine":[214],"proper":[216],"form":[225],"$(1-\\epsilon)$-approximate":[227,258],"CIVDs":[228,259],"small":[231],"$\\epsilon>0$.":[233],"Particularly,":[234],"consider":[236],"two":[237],"representative":[238],"problems,":[240],"vector":[241],"density-based":[244],"show":[247],"both":[249],"them":[251],"admit":[252],"fast":[253],"algorithms;":[255],"consequently,":[256],"can":[260],"be":[261],"built":[262],"$O(n":[264,267],"\\log^{\\max\\{3,d+1\\}}n)$":[265],"\\log^{2}":[268],"respectively.":[271]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
