{"id":"https://openalex.org/W4300486565","doi":"https://doi.org/10.48550/arxiv.2208.03829","title":"Revisiting Random Points: Combinatorial Complexity and Algorithms","display_name":"Revisiting Random Points: Combinatorial Complexity and Algorithms","publication_year":2022,"publication_date":"2022-08-07","ids":{"openalex":"https://openalex.org/W4300486565","doi":"https://doi.org/10.48550/arxiv.2208.03829"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2208.03829","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.03829","pdf_url":"https://arxiv.org/pdf/2208.03829","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2208.03829","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040577923","display_name":"Sariel Har-Peled","orcid":"https://orcid.org/0000-0003-2638-9635"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Har-Peled, Sariel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091358318","display_name":"Elfarouk Harb","orcid":"https://orcid.org/0000-0002-7770-0932"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harb, Elfarouk","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":true,"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9922999739646912,"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/T12288","display_name":"Optimization and Search Problems","score":0.9815999865531921,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.8165451288223267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7080138921737671},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7047122716903687},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.5424521565437317},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.5420367121696472},{"id":"https://openalex.org/keywords/minimum-weight-triangulation","display_name":"Minimum-weight triangulation","score":0.5380498766899109},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5325614213943481},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5027675628662109},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.48718661069869995},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.47480785846710205},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43470314145088196},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4275559186935425},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4228402078151703},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42005980014801025},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41387107968330383},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40930888056755066},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.24731314182281494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16220149397850037}],"concepts":[{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.8165451288223267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7080138921737671},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7047122716903687},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.5424521565437317},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5420367121696472},{"id":"https://openalex.org/C39969762","wikidata":"https://www.wikidata.org/wiki/Q6865406","display_name":"Minimum-weight triangulation","level":4,"score":0.5380498766899109},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5325614213943481},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5027675628662109},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.48718661069869995},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.47480785846710205},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43470314145088196},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4275559186935425},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4228402078151703},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42005980014801025},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41387107968330383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40930888056755066},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.24731314182281494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16220149397850037},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2208.03829","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.03829","pdf_url":"https://arxiv.org/pdf/2208.03829","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2208.03829","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2208.03829","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:arXiv.org:2208.03829","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.03829","pdf_url":"https://arxiv.org/pdf/2208.03829","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4943479214","display_name":"NSF-BSF: AF: Small: New directions in geometric traversal theory","funder_award_id":"2317241","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4300486565.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W113718658","https://openalex.org/W2350914983","https://openalex.org/W4302417997","https://openalex.org/W2375623303","https://openalex.org/W2348486108","https://openalex.org/W2380307509","https://openalex.org/W2374493932","https://openalex.org/W2381084059","https://openalex.org/W2094100801","https://openalex.org/W2172589357"],"abstract_inverted_index":{"Consider":[0],"a":[1,14,20,33,40,54,116,149],"set":[2,22],"$P$":[3,52,128],"of":[4,47,49,51,94,97,110,123,127,143],"$n$":[5],"points":[6,50,96],"picked":[7],"uniformly":[8],"and":[9,90,137,140],"independently":[10],"from":[11],"$[0,1]^d$":[12],"for":[13,32,154,159],"constant":[15],"dimension":[16],"$d$":[17],"--":[18,59,131],"such":[19],"point":[21],"is":[23,102,129,135],"extremely":[24],"well":[25],"behaved":[26],"in":[27,66],"many":[28],"aspects.":[29],"For":[30],"example,":[31],"fixed":[34],"$r":[35],"\\in":[36],"[0,1]$,":[37],"we":[38,60,147],"prove":[39],"new":[41,117,133],"concentration":[42],"result":[43],"on":[44],"the":[45,85,91,95,120,124,132,155],"number":[46,64],"pairs":[48],"at":[53,56],"distance":[55,156],"most":[57],"$r$":[58],"show":[61],"that":[62,69,119],"this":[63],"lies":[65],"an":[67,103],"interval":[68],"contains":[70],"only":[71],"$O(n":[72],"\\log":[73],"n)$":[74],"numbers.":[75],"We":[76,113],"also":[77,114],"present":[78,148],"simple":[79,150],"linear":[80,130],"time":[81,152],"algorithms":[82],"to":[83],"construct":[84],"Delaunay":[86,125],"triangulation,":[87],"Euclidean":[88],"MST,":[89],"convex":[92],"hull":[93],"$P$.":[98],"The":[99],"MST":[100],"algorithm":[101,106,153],"interesting":[104],"divide-and-conquer":[105],"which":[107],"might":[108,141],"be":[109,142],"independent":[111,144],"interest.":[112,145],"provide":[115],"proof":[118,134],"expected":[121],"complexity":[122],"triangulation":[126],"simpler":[136],"more":[138],"direct,":[139],"Finally,":[146],"$\\tilde{O}(n^{4/3})$":[151],"selection":[157],"problem":[158],"$d=2$.":[160]},"counts_by_year":[],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}