{"id":"https://openalex.org/W2991021809","doi":"https://doi.org/10.20382/jocg.v11i1a9","title":"Expected complexity of routing in $\\Theta_6$ and half-$\\Theta_6$ graphs","display_name":"Expected complexity of routing in $\\Theta_6$ and half-$\\Theta_6$ graphs","publication_year":2019,"publication_date":"2019-11-29","ids":{"openalex":"https://openalex.org/W2991021809","doi":"https://doi.org/10.20382/jocg.v11i1a9","mag":"2991021809"},"language":"en","primary_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3099","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3099","pdf_url":"https://jocg.org/index.php/jocg/article/view/3099","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 1 (2020); 212\u2013234","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://jocg.org/index.php/jocg/article/view/3099","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":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Bose, Prosenjit","raw_affiliation_strings":["Carleton University"],"affiliations":[{"raw_affiliation_string":"Carleton University","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042440491","display_name":"Jean-Lou De Carufel","orcid":"https://orcid.org/0000-0002-6734-8234"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"De Carufel, Jean-Lou","raw_affiliation_strings":["University of Ottawa [Ottawa]"],"affiliations":[{"raw_affiliation_string":"University of Ottawa [Ottawa]","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043040182","display_name":"Olivier Devillers","orcid":"https://orcid.org/0000-0003-4275-5068"},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Devillers, Olivier","raw_affiliation_strings":["Geometric Algorithms and Models Beyond the Linear and Euclidean realm"],"affiliations":[{"raw_affiliation_string":"Geometric Algorithms and Models Beyond the Linear and Euclidean realm","institution_ids":["https://openalex.org/I4210099593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013674788"],"corresponding_institution_ids":["https://openalex.org/I67031392"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.23132443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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":0.9919999837875366,"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":0.4950532019138336},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.45188698172569275},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3861255645751953},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2896294593811035},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.07243305444717407}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4950532019138336},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.45188698172569275},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3861255645751953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2896294593811035},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.07243305444717407}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:ojs.library.carleton.ca:article/3099","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3099","pdf_url":"https://jocg.org/index.php/jocg/article/view/3099","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 1 (2020); 212\u2013234","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-02338733v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-02338733","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] INRIA. 2019, pp.18","raw_type":"Reports"},{"id":"pmh:oai:HAL:hal-02479502v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-02479502","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EuroCG 2020 - 36th European Workshop on Computational Geometry, Mar 2020, W\u00fcrzburg, Germany","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:hal-02922660v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-02922660","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://journals.carleton.ca/jocg/index.php/jocg/article/view/484","raw_type":"Journal articles"},{"id":"doi:10.20382/jocg.v11i1a9","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v11i1a9","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"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-journal"}],"best_oa_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3099","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3099","pdf_url":"https://jocg.org/index.php/jocg/article/view/3099","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 1 (2020); 212\u2013234","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5438625379","display_name":null,"funder_award_id":"ANR-17-CE40-0017","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2991021809.pdf","grobid_xml":"https://content.openalex.org/works/W2991021809.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W1974891317","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2069964982","https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620"],"abstract_inverted_index":{"We":[0,74],"study":[1],"online":[2,40,115,213,232],"routing":[3,41,79,98,116,121,132,159,165,191,196,201,214,219,227,233,246,254,282,291],"algorithms":[4,80,278],"on":[5,71,106],"the":[6,9,18,32,63,85,96,101,112,135,138,150,170,189,199,209,266,269,273],"$\\Theta_6$-graph":[7,33,102],"and":[8,26,88,103,127,142,155,176,178,223,250],"half-$\\Theta_6$-graph":[10,104],"(which":[11],"is":[12,53,60,134,172,185,198,261,285],"equivalent":[13],"to":[14,49,264],"a":[15,22,27,38,45,107,162,224,237,251],"variant":[16],"of":[17,95,123,137,167,193,206,221,229,240,248,256,268,272,276,293],"Delaunay":[19],"triangulation).":[20],"Given":[21],"source":[23],"vertex":[24,29],"$s$":[25,48,126,141,154,175],"target":[28],"$t$":[30,50,128,143,177],"in":[31,62,84],"(resp.":[34,57],"half-$\\Theta_6$-graph),":[35],"there":[36],"exists":[37],"deterministic":[39],"algorithm":[42,117,147,160,215,234],"that":[43,81,235,284],"finds":[44],"path":[46],"from":[47],"whose":[51],"length":[52,136],"at":[54],"most":[55],"$2\\|st\\|$":[56],"$2.89\\|st\\|$)":[58],"which":[59,90],"optimal":[61,83],"worst":[64,86],"case":[65,87],"[Bose":[66],"et":[67],"al,":[68],"SIAM":[69],"J.":[70],"Computing,":[72],"44(6)].":[73],"propose":[75],"alternative,":[76],"slightly":[77],"simpler":[78],"are":[82,129,182],"for":[89,100,173],"we":[91],"provide":[92],"an":[93,119,217,244,280],"analysis":[94],"average":[97],"ratio":[99,192,197,292],"defined":[105],"Poisson":[108],"point":[109,271],"process.":[110],"For":[111,208],"$\\Theta_6$-graph,":[113],"our":[114,146,158,211],"has":[118,161,216,243],"expected":[120,164,218,226,245,253,281],"factor":[122,133,166,202,220,228,247,255,283],"$1.161$":[124],"when":[125],"random.":[130,183],"The":[131,195,258],"route":[139],"between":[140,153],"produced":[144],"by":[145,149],"divided":[148],"Euclidean":[151],"distance":[152],"$t$.":[156],"Moreover,":[157],"maximum":[163,171,200,225,252],"$1.22$,":[168],"where":[169],"fixed":[174],"all":[179,204],"other":[180],"points":[181],"This":[184],"much":[186,286],"better":[187,287],"than":[188,288],"worst-case":[190,290],"$2$.":[194],"among":[203],"pairs":[205],"points.":[207],"half-$\\Theta_6$-graph,":[210],"memoryless":[212],"$1.43$":[222],"$1.58$.":[230],"Our":[231],"uses":[236],"constant":[238],"amount":[239],"additional":[241,259],"memory":[242,260],"$1.34$":[249],"$1.40$.":[257],"only":[262],"used":[263],"remember":[265],"coordinates":[267],"starting":[270],"route.":[274],"Both":[275],"these":[277],"have":[279],"their":[289],"$2.89$.":[294]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}