{"id":"https://openalex.org/W7131382063","doi":"https://doi.org/10.48550/arxiv.2602.18980","title":"On Voronoi diagrams in the Funk Conical Geometry","display_name":"On Voronoi diagrams in the Funk Conical Geometry","publication_year":2026,"publication_date":"2026-02-21","ids":{"openalex":"https://openalex.org/W7131382063","doi":"https://doi.org/10.48550/arxiv.2602.18980"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.18980","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18980","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.18980","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126731429","display_name":"Aditya Acharya","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Acharya, Aditya","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126728695","display_name":"Auguste Henry Gezalyan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gezalyan, Auguste Henry","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016442699","display_name":"David M. Mount","orcid":"https://orcid.org/0000-0002-3290-8932"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mount, David M.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126691709","display_name":"Danesh Sivakumar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sivakumar, Danesh","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5126731429"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.275299996137619,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.275299996137619,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.21490000188350677,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.1624000072479248,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/voronoi-diagram","display_name":"Voronoi diagram","score":0.9232000112533569},{"id":"https://openalex.org/keywords/power-diagram","display_name":"Power diagram","score":0.59170001745224},{"id":"https://openalex.org/keywords/funk","display_name":"Funk","score":0.5824999809265137},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.5099999904632568},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.41909998655319214},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.41359999775886536},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3903000056743622},{"id":"https://openalex.org/keywords/medial-axis","display_name":"Medial axis","score":0.35920000076293945}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.9232000112533569},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6118000149726868},{"id":"https://openalex.org/C20573064","wikidata":"https://www.wikidata.org/wiki/Q13410436","display_name":"Power diagram","level":3,"score":0.59170001745224},{"id":"https://openalex.org/C147120446","wikidata":"https://www.wikidata.org/wiki/Q164444","display_name":"Funk","level":2,"score":0.5824999809265137},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.5099999904632568},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4406000077724457},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C185877587","wikidata":"https://www.wikidata.org/wiki/Q1757407","display_name":"Medial axis","level":2,"score":0.35920000076293945},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C124961601","wikidata":"https://www.wikidata.org/wiki/Q2518149","display_name":"Conical surface","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3027999997138977},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.302700012922287},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.2915000021457672},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2851000130176544},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.28279998898506165},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2630000114440918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25769999623298645},{"id":"https://openalex.org/C20468658","wikidata":"https://www.wikidata.org/wiki/Q17130624","display_name":"Weighted Voronoi diagram","level":3,"score":0.25690001249313354}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.18980","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18980","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.18980","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18980","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.7642768025398254,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"forward":[1,35,73,87],"and":[2,23,36,42,66,119,123],"reverse":[3,37],"Funk":[4,38,76,90,168],"weak":[5],"metrics":[6,39,77,91],"are":[7,78],"fundamental":[8],"distance":[9],"functions":[10],"on":[11,92],"convex":[12],"bodies":[13],"that":[14],"serve":[15],"as":[16],"the":[17,21,34,61,64,71,85,97,162,167],"building":[18],"blocks":[19],"for":[20,107,128],"Hilbert":[22],"Thompson":[24],"metrics.":[25,169],"In":[26],"this":[27],"paper":[28],"we":[29,101],"study":[30],"Voronoi":[31,68,82,140],"diagrams":[32,69,83,110],"under":[33],"in":[40,70,84,111,155],"polygonal":[41,130],"elliptical":[43,113],"cones.":[44,157],"We":[45,142],"establish":[46],"several":[47],"key":[48],"geometric":[49],"properties:":[50],"(1)":[51],"bisectors":[52],"consist":[53],"of":[54,57,63,96,148,161,166],"a":[55,116,136,145,153],"set":[56],"rays":[58],"emanating":[59],"from":[60,120],"apex":[62],"cone,":[65],"(2)":[67],"$d$-dimensional":[72,112],"(or":[74,88],"reverse)":[75,89],"equivalent":[79],"to":[80,118,138],"additively-weighted":[81],"$(d-1)$-dimensional":[86],"bounded":[93],"cross":[94],"sections":[95],"cone.":[98],"Leveraging":[99],"this,":[100],"provide":[102,144],"an":[103,124],"$O\\big(n^{\\ceil{\\frac{d-1}{2}}+1}\\big)$":[104],"time":[105,126],"algorithm":[106,127],"creating":[108],"these":[109],"cones":[114,131],"using":[115],"transformation":[117],"Apollonius":[121],"diagrams,":[122],"$O(mn\\log(n))$":[125],"3-dimensional":[129,156],"with":[132],"$m$":[133],"facets":[134],"via":[135],"reduction":[137],"abstract":[139],"diagrams.":[141],"also":[143],"complete":[146],"characterization":[147],"when":[149],"three":[150],"sites":[151],"have":[152],"circumcenter":[154],"This":[158],"is":[159],"one":[160],"first":[163],"algorithmic":[164],"studies":[165]},"counts_by_year":[],"updated_date":"2026-02-26T06:34:08.959763","created_date":"2026-02-26T00:00:00"}
