{"id":"https://openalex.org/W2022845172","doi":"https://doi.org/10.1137/110832458","title":"The Stretch Factor of the Delaunay Triangulation Is Less than 1.998","display_name":"The Stretch Factor of the Delaunay Triangulation Is Less than 1.998","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2022845172","doi":"https://doi.org/10.1137/110832458","mag":"2022845172"},"language":"en","primary_location":{"id":"doi:10.1137/110832458","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832458","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1103.4361","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ge Xia","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ge Xia","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.5152,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.96820175,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"42","issue":"4","first_page":"1620","last_page":"1659"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.988099992275238,"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":0.988099992275238,"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":0.0032999999821186066,"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":0.00139999995008111,"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/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.9251999855041504},{"id":"https://openalex.org/keywords/pitteway-triangulation","display_name":"Pitteway triangulation","score":0.7386000156402588},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.6966999769210815},{"id":"https://openalex.org/keywords/minimum-weight-triangulation","display_name":"Minimum-weight triangulation","score":0.6401000022888184},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6205999851226807},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.5914999842643738},{"id":"https://openalex.org/keywords/spanner","display_name":"Spanner","score":0.5906999707221985},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.498199999332428}],"concepts":[{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.9251999855041504},{"id":"https://openalex.org/C178609930","wikidata":"https://www.wikidata.org/wiki/Q3538712","display_name":"Pitteway triangulation","level":3,"score":0.7386000156402588},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.710099995136261},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.6966999769210815},{"id":"https://openalex.org/C39969762","wikidata":"https://www.wikidata.org/wiki/Q6865406","display_name":"Minimum-weight triangulation","level":4,"score":0.6401000022888184},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6205999851226807},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.604200005531311},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.5914999842643738},{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.5906999707221985},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.498199999332428},{"id":"https://openalex.org/C50285192","wikidata":"https://www.wikidata.org/wiki/Q15713605","display_name":"Surface triangulation","level":4,"score":0.4740000069141388},{"id":"https://openalex.org/C167117609","wikidata":"https://www.wikidata.org/wiki/Q17078161","display_name":"Point set triangulation","level":3,"score":0.4691999852657318},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C170836113","wikidata":"https://www.wikidata.org/wiki/Q5406126","display_name":"Euclidean shortest path","level":5,"score":0.37790000438690186},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34769999980926514},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.28870001435279846},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2874999940395355},{"id":"https://openalex.org/C99886907","wikidata":"https://www.wikidata.org/wiki/Q105742691","display_name":"Ruppert's algorithm","level":4,"score":0.2784000039100647},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.2736000120639801},{"id":"https://openalex.org/C183342303","wikidata":"https://www.wikidata.org/wiki/Q105742691","display_name":"Chew's second algorithm","level":4,"score":0.27129998803138733},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2549000084400177}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110832458","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832458","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"},{"id":"pmh:oai:arXiv.org:1103.4361","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1103.4361","pdf_url":"https://arxiv.org/pdf/1103.4361","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1103.4361","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1103.4361","pdf_url":"https://arxiv.org/pdf/1103.4361","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1496496117","https://openalex.org/W1993585122","https://openalex.org/W2004476837","https://openalex.org/W2018527525","https://openalex.org/W2031874971","https://openalex.org/W2038433986","https://openalex.org/W2113604744","https://openalex.org/W2139391136","https://openalex.org/W2153410375","https://openalex.org/W2786889022"],"related_works":[],"abstract_inverted_index":{"Let":[0,12],"$S$":[1],"be":[2,14,153],"a":[3,15,61,74,156,160,173],"finite":[4],"set":[5],"of":[6,18,30,44,68,90,107,124,139,146,159,179,182,191],"points":[7,38],"in":[8,42,53,78,122,188],"the":[9,33,45,56,65,69,87,91,102,118,125,143,147,177,189],"Euclidean":[10,57,120,161,183],"plane.":[11],"$D$":[13,31,54],"Delaunay":[16,70,92,114],"triangulation":[17,71,93,115],"$S$.":[19],"The":[20],"stretch":[21,66,88,149],"factor":[22,67,89,150],"(also":[23],"known":[24],"as":[25],"dilation":[26],"or":[27],"spanning":[28],"ratio)":[29],"is":[32,94,168],"maximum":[34],"ratio,":[35],"among":[36],"all":[37],"$p$":[39,50],"and":[40,111,130],"$q$":[41,52],"$S$,":[43],"shortest":[46],"path":[47],"distance":[48,58],"from":[49],"to":[51],"over":[55],"$||pq||$.":[59],"Proving":[60],"tight":[62],"bound":[63,106,138,145,167],"on":[64,128,176],"has":[72,172,186],"been":[73],"long-standing":[75],"open":[76],"problem":[77,178],"computational":[79],"geometry.":[80],"In":[81],"this":[82],"paper":[83],"we":[84],"prove":[85],"that":[86,151],"less":[95],"than":[96],"$\\rho":[97],"=":[98],"1.998$,":[99],"significantly":[100],"improving":[101],"current":[103,164],"best":[104,148,165],"upper":[105,144,166],"2.42":[108],"by":[109,155],"Keil":[110],"Gutwin":[112],"[``The":[113],"closely":[116],"approximates":[117],"complete":[119],"graph,\u201d":[121],"Proceedings":[123],"1st":[126],"Workshop":[127],"Algorithms":[129],"Data":[131],"Structures":[132],"(WADS),":[133],"1989,":[134],"pp.":[135],"47--56].":[136],"Our":[137,170],"1.998":[140],"also":[141],"improves":[142],"can":[152],"achieved":[154],"plane":[157],"spanner":[158],"graph":[162],"(the":[163],"2).":[169],"result":[171],"direct":[174],"impact":[175],"constructing":[180],"spanners":[181],"graphs,":[184],"which":[185],"applications":[187],"area":[190],"wireless":[192],"computing.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}