{"id":"https://openalex.org/W4367860431","doi":"https://doi.org/10.20382/jocg.v16i2a5","title":"A Quadtree, a Steiner Spanner, and Approximate Nearest Neighbours in Hyperbolic Space","display_name":"A Quadtree, a Steiner Spanner, and Approximate Nearest Neighbours in Hyperbolic Space","publication_year":2023,"publication_date":"2023-05-02","ids":{"openalex":"https://openalex.org/W4367860431","doi":"https://doi.org/10.20382/jocg.v16i2a5"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2305.01356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.01356","pdf_url":"https://arxiv.org/pdf/2305.01356","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2305.01356","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057527289","display_name":"\u202aS\u00e1ndor Kisfaludi-Bak","orcid":"https://orcid.org/0000-0002-6856-2902"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Kisfaludi-Bak, S\u00e1ndor","raw_affiliation_strings":["Aalto University"],"raw_orcid":"https://orcid.org/0000-0002-6856-2902","affiliations":[{"raw_affiliation_string":"Aalto University","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028724460","display_name":"Geert van Wordragen","orcid":"https://orcid.org/0000-0002-2650-638X"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"van Wordragen, Geert","raw_affiliation_strings":["Aalto University"],"raw_orcid":"https://orcid.org/0000-0002-2650-638X","affiliations":[{"raw_affiliation_string":"Aalto University","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.9994999766349792,"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":0.9994999766349792,"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/T11870","display_name":"Structural Analysis and Optimization","score":0.9642999768257141,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9553999900817871,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spanner","display_name":"Spanner","score":0.8947227001190186},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7626221179962158},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6276158094406128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.561104416847229},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5564283132553101},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5425570011138916},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.529165506362915},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.42734256386756897},{"id":"https://openalex.org/keywords/hyperbolic-space","display_name":"Hyperbolic space","score":0.41832464933395386},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4135925769805908},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3711695671081543},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1651720106601715},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13911083340644836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12672093510627747}],"concepts":[{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.8947227001190186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7626221179962158},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6276158094406128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.561104416847229},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5564283132553101},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5425570011138916},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.529165506362915},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42734256386756897},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.41832464933395386},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4135925769805908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3711695671081543},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1651720106601715},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13911083340644836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12672093510627747},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"pmh:oai:arXiv.org:2305.01356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.01356","pdf_url":"https://arxiv.org/pdf/2305.01356","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:20013","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.68","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol293-socg2024/LIPIcs.SoCG.2024.68/LIPIcs.SoCG.2024.68.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/129020","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/1941b80c-6e81-40cd-9010-c2a01fba959b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401662","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/138345","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/227ee43c-946c-472e-bbad-54cddee0a5de","pdf_url":null,"source":{"id":"https://openalex.org/S4306401662","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2305.01356","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2305.01356","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.20382/jocg.v16i2a5","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v16i2a5","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"},{"id":"doi:10.4230/lipics.socg.2024.68","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2024.68","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2305.01356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.01356","pdf_url":"https://arxiv.org/pdf/2305.01356","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4367860431.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4297580473","https://openalex.org/W2949656589","https://openalex.org/W2398255676","https://openalex.org/W2026144971","https://openalex.org/W2774521735","https://openalex.org/W229853467","https://openalex.org/W2781495912","https://openalex.org/W1965038885","https://openalex.org/W2610298398","https://openalex.org/W2023081456"],"abstract_inverted_index":{"We":[0],"propose":[1,27],"a":[2,13,28,68,73,82,91,96,138,167],"data":[3,24,149,193,216],"structure":[4,25,150,194,217],"in":[5,18,43,62,142,151,185,187,218],"d-dimensional":[6,143],"hyperbolic":[7,32,63,144,219],"space":[8,145,220],"that":[9,71,85,122,172],"can":[10,86,165,198],"be":[11,87],"considered":[12],"natural":[14],"counterpart":[15],"to":[16,131],"quadtrees":[17,48],"Euclidean":[19,44],"spaces.":[20,45],"Based":[21],"on":[22],"this":[23],"we":[26,52,66,93,120,146,164],"so-called":[29],"L-order":[30,51],"for":[31,159],"point":[33,139,162,168,200],"sets,":[34],"which":[35],"is":[36,111,173,195,210],"an":[37,128],"extension":[38],"of":[39,76,102,116],"the":[40,50,99,103,107,132,148,192,211],"Z-order":[41],"defined":[42],"Using":[46],"these":[47],"and":[49,197,202],"build":[53,147],"geometric":[54],"spanners.":[55],"Near-linear":[56],"size":[57],"(1+\u03b5)-spanners":[58],"do":[59],"not":[60],"exist":[61],"spaces,":[64],"but":[65],"create":[67],"Steiner":[69,124],"spanner":[70,125],"achieves":[72],"spanning":[74,108],"ratio":[75,109],"1+\u03b5":[77,176],"with":[78,204,221],"O_{d,\u03b5}(n)":[79,156],"edges,":[80],"using":[81,155],"simple":[83],"construction":[84],"maintained":[88],"dynamically.":[89],"As":[90],"corollary":[92],"also":[94],"get":[95],"(2+\u03b5)-spanner":[97],"(in":[98],"classical":[100],"sense)":[101],"same":[104],"size,":[105],"where":[106],"2+\u03b5":[110],"almost":[112],"optimal":[113],"among":[114],"spanners":[115],"subquadratic":[117],"size.":[118],"Finally,":[119],"show":[121],"our":[123],"directly":[126],"provides":[127],"elegant":[129],"solution":[130],"approximate":[133],"nearest":[134,183,214],"neighbour":[135,184,215],"problem:":[136],"given":[137],"set":[140],"P":[141,171,186],"O_{d,\u03b5}(nlog":[152],"n)":[153,189],"time,":[154],"space.":[157],"Then":[158],"any":[160],"query":[161],"q":[163,180],"find":[166],"p":[169],"\u2208":[170],"at":[174],"most":[175],"times":[177],"farther":[178],"from":[179],"than":[181],"its":[182],"O_{d,\u03b5}(log":[188,207],"time.":[190],"Moreover,":[191],"dynamic":[196,213],"handle":[199],"insertions":[201],"deletions":[203],"update":[205],"time":[206],"n).":[208],"This":[209],"first":[212],"proven":[222],"efficiency":[223],"guarantees.":[224]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2023-05-04T00:00:00"}