{"id":"https://openalex.org/W2153726094","doi":"https://doi.org/10.1137/140988103","title":"Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral Triangles","display_name":"Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral Triangles","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2153726094","doi":"https://doi.org/10.1137/140988103","mag":"2153726094"},"language":"en","primary_location":{"id":"doi:10.1137/140988103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140988103","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://portal.findresearcher.sdu.dk/da/publications/f5b8a79d-6898-4c2c-8c84-64b2b4803cd2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013674788","display_name":"Prosenjit Bose","orcid":"https://orcid.org/0000-0002-8906-0573"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Prosenjit Bose","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021765002","display_name":"Rolf Fagerberg","orcid":"https://orcid.org/0000-0003-1004-3314"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rolf Fagerberg","raw_affiliation_strings":["Institut for Matematik og Datalogi"],"affiliations":[{"raw_affiliation_string":"Institut for Matematik og Datalogi","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042432858","display_name":"Andr\u00e9 van Renssen","orcid":"https://orcid.org/0000-0002-9294-9947"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andr\u00e9 van Renssen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074370405","display_name":"Sander Verdonschot","orcid":"https://orcid.org/0000-0002-7892-2561"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sander Verdonschot","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5013674788"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8996,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.80150215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"44","issue":"6","first_page":"1626","last_page":"1649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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":0.9993000030517578,"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/T12288","display_name":"Optimization and Search Problems","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9884999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7592747211456299},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.7213921546936035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6292935013771057},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4237819314002991},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4206807017326355},{"id":"https://openalex.org/keywords/equilateral-triangle","display_name":"Equilateral triangle","score":0.41367584466934204},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3733317255973816},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09142959117889404}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7592747211456299},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.7213921546936035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6292935013771057},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4237819314002991},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4206807017326355},{"id":"https://openalex.org/C146786541","wikidata":"https://www.wikidata.org/wiki/Q157002","display_name":"Equilateral triangle","level":2,"score":0.41367584466934204},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3733317255973816},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09142959117889404}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/140988103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140988103","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:sdu.dk:openaire/f5b8a79d-6898-4c2c-8c84-64b2b4803cd2","is_oa":true,"landing_page_url":"https://portal.findresearcher.sdu.dk/da/publications/f5b8a79d-6898-4c2c-8c84-64b2b4803cd2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400424","display_name":"University of Southern Denmark Research Portal (University of Southern Denmark)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177969490","host_organization_name":"University of Southern Denmark","host_organization_lineage":["https://openalex.org/I177969490"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bose, P, Fagerberg, R, Renssen, A V & Verdonschot, S 2015, 'Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral Triangles', SIAM Journal on Computing, vol. 44, no. 6, pp. 1626-1649. https://doi.org/10.1137/140988103","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1409.6397","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.6397","pdf_url":"https://arxiv.org/pdf/1409.6397","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"},{"id":"mag:2153726094","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1409.6397","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1409.6397","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1409.6397","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":"article"}],"best_oa_location":{"id":"pmh:oai:sdu.dk:openaire/f5b8a79d-6898-4c2c-8c84-64b2b4803cd2","is_oa":true,"landing_page_url":"https://portal.findresearcher.sdu.dk/da/publications/f5b8a79d-6898-4c2c-8c84-64b2b4803cd2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400424","display_name":"University of Southern Denmark Research Portal (University of Southern Denmark)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177969490","host_organization_name":"University of Southern Denmark","host_organization_lineage":["https://openalex.org/I177969490"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bose, P, Fagerberg, R, Renssen, A V & Verdonschot, S 2015, 'Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral Triangles', SIAM Journal on Computing, vol. 44, no. 6, pp. 1626-1649. https://doi.org/10.1137/140988103","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322928","display_name":"Danmarks Frie Forskningsfond","ror":"https://ror.org/02sptwz63"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W165089886","https://openalex.org/W1480586647","https://openalex.org/W1543674095","https://openalex.org/W1563817519","https://openalex.org/W1572848511","https://openalex.org/W1979472618","https://openalex.org/W1981505946","https://openalex.org/W1991764368","https://openalex.org/W1993306206","https://openalex.org/W1996086742","https://openalex.org/W2011958538","https://openalex.org/W2014505326","https://openalex.org/W2019729116","https://openalex.org/W2047215131","https://openalex.org/W2077005280","https://openalex.org/W2113604744","https://openalex.org/W2122870665","https://openalex.org/W2139391136","https://openalex.org/W2168630584","https://openalex.org/W2169273227","https://openalex.org/W2171151410","https://openalex.org/W2188440933"],"related_works":["https://openalex.org/W2963197342","https://openalex.org/W2242269073","https://openalex.org/W1806592748","https://openalex.org/W2951958562","https://openalex.org/W2889537410","https://openalex.org/W2592215285","https://openalex.org/W2295141444","https://openalex.org/W3003378376","https://openalex.org/W1976125024","https://openalex.org/W1549878614","https://openalex.org/W2160843890","https://openalex.org/W2963656439","https://openalex.org/W2068354545","https://openalex.org/W2397880522","https://openalex.org/W2032159439","https://openalex.org/W2067317911","https://openalex.org/W2556004932","https://openalex.org/W2016972645","https://openalex.org/W2568372686","https://openalex.org/W1858540722"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,12,20,68,100,116,131,176,198],"deterministic":[3],"local":[4,63,178],"routing":[5,64,70,76,119,179,191,199],"algorithm":[6,65,77,180,192],"that":[7,61,74,94],"is":[8,24,34,43,78,81,91,104],"guaranteed":[9],"to":[10,26,196],"find":[11,114],"path":[13,42,101,117],"between":[14,53],"any":[15],"pair":[16,55],"of":[17,40,56,88,154,201,210],"vertices":[18],"in":[19,127,152],"half-$\\theta_6$-graph":[21,23,90,132],"(the":[22],"equivalent":[25],"the":[27,31,41,50,54,85,89,108,128,150,155,211],"Delaunay":[28],"triangulation":[29,123],"where":[30],"empty":[32],"region":[33],"an":[35],"equilateral":[36],"triangle).":[37],"The":[38],"length":[39,103],"at":[44,105],"most":[45,106],"$5/\\sqrt{3}":[46],"\\approx":[47,203],"2.887$":[48],"times":[49],"Euclidean":[51,109],"distance":[52],"vertices.":[57],"Moreover,":[58],"we":[59,111,187],"show":[60,188],"no":[62],"can":[66,124,193],"achieve":[67],"better":[69],"ratio,":[71],"thereby":[72],"proving":[73],"our":[75,173,190],"optimal.":[79],"This":[80],"somewhat":[82],"surprising":[83],"because":[84],"spanning":[86],"ratio":[87,200],"2,":[92],"meaning":[93],"even":[95],"though":[96],"there":[97],"always":[98,113],"exists":[99],"whose":[102],"twice":[107],"distance,":[110],"cannot":[112],"such":[115,183],"when":[118],"locally.":[120],"Since":[121],"every":[122,182],"be":[125,194],"embedded":[126,184],"plane":[129],"as":[130],"using":[133],"$O(\\log":[134],"n)$":[135],"bits":[136],"per":[137],"vertex":[138],"coordinate":[139],"via":[140],"Schnyder's":[141],"embedding":[142],"scheme":[143],"[W.":[144],"Schnyder,":[145],"Embedding":[146],"planar":[147],"graphs":[148],"on":[149,160,205],"grid,":[151],"Proceedings":[153],"1st":[156],"Annual":[157],"ACM--SIAM":[158],"Symposium":[159],"Discrete":[161],"Algorithms":[162],"(SODA":[163],"1990),":[164],"ACM,":[165],"New":[166],"York,":[167],"SIAM,":[168],"Philadelphia,":[169],"1990,":[170],"pp.":[171],"138--148],":[172],"result":[174],"provides":[175],"competitive":[177],"for":[181],"triangulation.":[185],"Finally,":[186],"how":[189],"adapted":[195],"provide":[197],"$15/\\sqrt{3}":[202],"8.660$":[204],"two":[206],"bounded":[207],"degree":[208],"subgraphs":[209],"half-$\\theta_6$-graph.":[212]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2022-10-02T00:00:00"}