{"id":"https://openalex.org/W7135180609","doi":"https://doi.org/10.48550/arxiv.2603.11775","title":"Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain","display_name":"Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain","publication_year":2026,"publication_date":"2026-03-12","ids":{"openalex":"https://openalex.org/W7135180609","doi":"https://doi.org/10.48550/arxiv.2603.11775"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.11775","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11775","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.11775","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129032824","display_name":"Joost van der Laan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"van der Laan, Joost","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129036339","display_name":"Frank Staals","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Staals, Frank","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5129093329","display_name":"Lorenzo Theunissen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Theunissen, Lorenzo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5129032824"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.802299976348877,"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":0.802299976348877,"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":0.0560000017285347,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.020600000396370888,"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/k-nearest-neighbors-algorithm","display_name":"k-nearest neighbors algorithm","score":0.6844000220298767},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6051999926567078},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5641000270843506},{"id":"https://openalex.org/keywords/nearest-neighbor-search","display_name":"Nearest neighbor search","score":0.5633999705314636},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5515000224113464},{"id":"https://openalex.org/keywords/fixed-radius-near-neighbors","display_name":"Fixed-radius near neighbors","score":0.5307000279426575},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.5218999981880188},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5146999955177307},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4731000065803528}],"concepts":[{"id":"https://openalex.org/C113238511","wikidata":"https://www.wikidata.org/wiki/Q1071612","display_name":"k-nearest neighbors algorithm","level":2,"score":0.6844000220298767},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6051999926567078},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5641000270843506},{"id":"https://openalex.org/C116738811","wikidata":"https://www.wikidata.org/wiki/Q608751","display_name":"Nearest neighbor search","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5515000224113464},{"id":"https://openalex.org/C46264003","wikidata":"https://www.wikidata.org/wiki/Q5456333","display_name":"Fixed-radius near neighbors","level":5,"score":0.5307000279426575},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.5218999981880188},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5146999955177307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4846000075340271},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4731000065803528},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4713999927043915},{"id":"https://openalex.org/C90988772","wikidata":"https://www.wikidata.org/wiki/Q2855103","display_name":"Nearest neighbor graph","level":3,"score":0.4456000030040741},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4422999918460846},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.42719998955726624},{"id":"https://openalex.org/C53661774","wikidata":"https://www.wikidata.org/wiki/Q13108095","display_name":"Cover tree","level":5,"score":0.41659998893737793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38839998841285706},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.38019999861717224},{"id":"https://openalex.org/C161986146","wikidata":"https://www.wikidata.org/wiki/Q4896845","display_name":"Best bin first","level":3,"score":0.375},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3093999922275543},{"id":"https://openalex.org/C186750021","wikidata":"https://www.wikidata.org/wiki/Q7208210","display_name":"Point location","level":3,"score":0.3010999858379364},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C2988382989","wikidata":"https://www.wikidata.org/wiki/Q370685","display_name":"Data space","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C102164700","wikidata":"https://www.wikidata.org/wiki/Q17162702","display_name":"Nearest-neighbor chain algorithm","level":5,"score":0.263700008392334},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.2565000057220459}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.11775","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11775","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":"doi:10.48550/arxiv.2603.11775","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11775","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,58],"present":[1],"efficient":[2],"data":[3,111,142,190],"structures":[4],"for":[5,95],"approximate":[6,11],"nearest":[7,175],"neighbor":[8,176],"searching":[9],"and":[10,63,123,162,172],"2-point":[12],"shortest":[13],"path":[14],"queries":[15],"in":[16,38,65,125,177,194],"a":[17,30,46,88,100,116,149],"two-dimensional":[18],"polygonal":[19],"domain":[20],"$P$":[21,39],"with":[22],"$n$":[23],"vertices.":[24],"Our":[25,189],"goal":[26],"is":[27,164],"to":[28,52,147],"store":[29],"dynamic":[31],"set":[32,67],"of":[33,68,82,91,118],"$m$":[34],"point":[35,56,160],"sites":[36,69],"$S$":[37],"so":[40,154],"that":[41,113,144,155],"we":[42,93,105,132],"can":[43,114],"efficiently":[44],"find":[45],"site":[47,150],"$s":[48,151],"\\in":[49,85,152],"S$":[50,153],"closest":[51],"an":[53,79,107,135],"arbitrary":[54,80],"query":[55,159],"$q$.":[57],"will":[59],"allow":[60,94],"both":[61],"insertions":[62],"deletions":[64],"the":[66,76,97,119,156,168],"$S$.":[70],"However,":[71],"as":[72],"even":[73],"just":[74],"computing":[75],"distance":[77,120,157,169],"between":[78,121,158,170],"pair":[81],"points":[83],"$q,s":[84],"P$":[86],"requires":[87],"substantial":[89],"amount":[90],"space,":[92],"approximating":[96],"distances.":[98],"Given":[99],"parameter":[101],"$\\varepsilon":[102],">":[103],"0$,":[104],"build":[106],"$O(\\frac{n}{\\varepsilon}\\log":[108],"n)$":[109,127],"space":[110,141],"structure":[112,143,191],"compute":[115],"$1+\\varepsilon$-approximation":[117],"$q$":[122,161,171],"$s$":[124,163],"$O(\\frac{1}{\\varepsilon^2}\\log":[126,178,195],"time.":[128,188,206],"Building":[129],"on":[130],"this,":[131],"then":[133],"obtain":[134],"$O(\\frac{n+m}{\\varepsilon}\\log":[136],"n":[137,179,182,196,199],"+":[138,180,185,197,202],"\\frac{m}{\\varepsilon}\\log":[139],"m)$":[140,187,204],"allows":[145],"us":[146],"report":[148],"at":[165],"most":[166],"$(1+\\varepsilon)$-times":[167],"its":[173],"true":[174],"\\frac{1}{\\varepsilon}\\log":[181,198],"\\log":[183,200],"m":[184,201],"\\frac{1}{\\varepsilon}\\log^2":[186,203],"supports":[192],"updates":[193],"amortized":[205]},"counts_by_year":[],"updated_date":"2026-03-14T06:46:50.379900","created_date":"2026-03-14T00:00:00"}