{"id":"https://openalex.org/W7160023696","doi":"https://doi.org/10.48550/arxiv.2605.00743","title":"Smallest Enclosing Disk Queries Using Farthest-Point Voronoi Diagrams","display_name":"Smallest Enclosing Disk Queries Using Farthest-Point Voronoi Diagrams","publication_year":2026,"publication_date":"2026-05-01","ids":{"openalex":"https://openalex.org/W7160023696","doi":"https://doi.org/10.48550/arxiv.2605.00743"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.00743","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00743","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.00743","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077490455","display_name":"Kevin Buchin","orcid":"https://orcid.org/0000-0002-3022-7877"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Buchin, Kevin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135263018","display_name":"Mark Joachim Krallmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krallmann, Mark Joachim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135213387","display_name":"Frank Staals","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Staals, Frank","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.935699999332428,"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":0.935699999332428,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.016100000590085983,"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":0.0066999997943639755,"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/voronoi-diagram","display_name":"Voronoi diagram","score":0.8619999885559082},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.6018999814987183},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5843999981880188},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.5016000270843506},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.3668999969959259},{"id":"https://openalex.org/keywords/query-optimization","display_name":"Query optimization","score":0.357699990272522},{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.3422999978065491},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.34200000762939453}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8619999885559082},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.6018999814987183},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5843999981880188},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.5016000270843506},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48539999127388},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4336000084877014},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41990000009536743},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C157692150","wikidata":"https://www.wikidata.org/wiki/Q2919848","display_name":"Query optimization","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3492000102996826},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.3422999978065491},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C2989070954","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database query","level":2,"score":0.34130001068115234},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32100000977516174},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C172722865","wikidata":"https://www.wikidata.org/wiki/Q2302053","display_name":"Spatial query","level":5,"score":0.2863999903202057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28209999203681946},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.27559998631477356},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C136736807","wikidata":"https://www.wikidata.org/wiki/Q818943","display_name":"Range query (database)","level":5,"score":0.2540000081062317},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.00743","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00743","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.00743","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00743","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0],"$S$":[1,15,27],"be":[2],"a":[3,42,73,91],"set":[4],"of":[5,23,45,95,105],"$n$":[6],"points":[7,25,59],"in":[8,26],"$\\mathbb{R}^2$.":[9],"Our":[10,88],"goal":[11],"is":[12],"to":[13,16,60],"preprocess":[14],"efficiently":[17],"compute":[18],"the":[19,24,58,111],"smallest":[20],"enclosing":[21],"disk":[22],"that":[28],"lie":[29],"inside":[30],"an":[31,101],"axis-aligned":[32],"query":[33,43,93,103],"rectangle.":[34],"Previous":[35],"data":[36],"structures":[37],"for":[38],"this":[39],"problem":[40],"achieve":[41],"time":[44,53,94,104],"$O(\\log^6":[46],"n)$":[47,51,97,109],"with":[48,110],"$O(n":[49],"\\log^2":[50],"preprocessing":[52,113],"and":[54,66],"space":[55],"by":[56],"lifting":[57],"3D,":[61],"dualizing":[62],"them":[63],"into":[64],"polyhedra,":[65],"searching":[67],"through":[68],"their":[69],"intersections.":[70],"We":[71],"present":[72],"significantly":[74],"simpler":[75],"approach,":[76],"solely":[77],"based":[78],"on":[79],"2D":[80,84],"geometric":[81],"structures,":[82],"specifically":[83],"farthest-point":[85],"Voronoi":[86],"diagrams.":[87],"approach":[89],"achieves":[90],"deterministic":[92],"$O(\\log^4":[96],"and,":[98],"via":[99],"randomization,":[100],"expected":[102],"$O(\\log^{5/2}":[106],"n":[107],"\\log\\log":[108],"same":[112],"bounds.":[114]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-05T00:00:00"}
