{"id":"https://openalex.org/W7162534027","doi":"https://doi.org/10.4230/lipics.socg.2026.4","title":"Dynamic Nearest-Neighbor Searching Under General Metrics in \u211d\u00b3 and Its Applications","display_name":"Dynamic Nearest-Neighbor Searching Under General Metrics in \u211d\u00b3 and Its Applications","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162534027","doi":"https://doi.org/10.4230/lipics.socg.2026.4"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25810","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.4","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.4/LIPIcs.SoCG.2026.4.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":null,"raw_type":"InProceedings"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.4/LIPIcs.SoCG.2026.4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048240641","display_name":"Pankaj Agarwal","orcid":"https://orcid.org/0000-0001-5876-6998"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Agarwal, Pankaj K.","raw_affiliation_strings":["Department of Computer Science, Duke University, Durham, NC, USA"],"raw_orcid":"https://orcid.org/0000-0002-9439-181X","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104278282","display_name":"Matthew J. Katz","orcid":"https://orcid.org/0000-0002-5971-6746"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Katz, Matthew J.","raw_affiliation_strings":["The Stein Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer Sheva, Israel"],"raw_orcid":"https://orcid.org/0000-0002-0672-729X","affiliations":[{"raw_affiliation_string":"The Stein Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Sharir, Micha","raw_affiliation_strings":["School of Computer Science, Tel Aviv University, Tel Aviv, Israel"],"raw_orcid":"https://orcid.org/0000-0002-2541-3763","affiliations":[{"raw_affiliation_string":"School of Computer Science, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.62892768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.6488999724388123,"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":0.6488999724388123,"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":0.131400004029274,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.05050000175833702,"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/graph","display_name":"Graph","score":0.5877000093460083},{"id":"https://openalex.org/keywords/homothetic-transformation","display_name":"Homothetic transformation","score":0.5802000164985657},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.44339999556541443},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.42260000109672546},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.40860000252723694},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4050000011920929},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3953000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6625999808311462},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.618399977684021},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5877000093460083},{"id":"https://openalex.org/C91709909","wikidata":"https://www.wikidata.org/wiki/Q583960","display_name":"Homothetic transformation","level":2,"score":0.5802000164985657},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.429500013589859},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.42260000109672546},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4050000011920929},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33169999718666077},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25810","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.4","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.4/LIPIcs.SoCG.2026.4.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":null,"raw_type":"InProceedings"},{"id":"doi:10.4230/lipics.socg.2026.4","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.4","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:drops-oai.dagstuhl.de:25810","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.4","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.4/LIPIcs.SoCG.2026.4.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":null,"raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162534027.pdf","grobid_xml":"https://content.openalex.org/works/W7162534027.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0,29,175],"K":[1],"be":[2,31,58,114,127,195,221,252],"a":[3,12,23,32,50,65,74,96,99,213,237],"compact,":[4],"centrally-symmetric,":[5],"strictly-convex":[6],"region":[7],"in":[8,60,116,129,140,197,212,223,243,254],"\u211d\u00b3,":[9,244],"which":[10],"is":[11,111,161],"semi-algebraic":[13],"set":[14,33],"of":[15,22,34,38,46,68,78,89,105,122,153,169,181,218],"constant":[16,168],"complexity,":[17],"i.e.":[18],"the":[19,103,135,148,154,167,178,184,205,209],"unit":[20],"ball":[21],"corresponding":[24],"metric,":[25],"denoted":[26],"as":[27,230,232],"\u2016\u22c5\u2016_K.":[28],"\ud835\udca6":[30,56,106,123,219],"n":[35,241],"homothetic":[36],"copies":[37],"K.":[39],"This":[40],"paper":[41],"contains":[42],"two":[43],"main":[44],"sets":[45],"results:":[47],"(i)":[48],"For":[49],"storage":[51],"parameter":[52],"s":[53],"\u2208":[54],"[n,n\u00b3],":[55],"can":[57,113,126,194,220,250],"preprocessed":[59],"O^*(s)":[61],"expected":[62,143,199,225],"time":[63,144],"into":[64],"data":[66,136,186],"structure":[67,137],"size":[69],"O^*(s),":[70],"so":[71],"that":[72],"for":[73],"query":[75,82,101],"homothet":[76],"K\u2080":[77,85,110,125],"K,":[79],"an":[80,162],"intersection-detection":[81],"(determine":[83],"whether":[84],"intersects":[86],"any":[87],"member":[88,104],"\ud835\udca6,":[90],"and":[91,166],"if":[92],"so,":[93],"report":[94],"such":[95],"member)":[97],"or":[98,189],"nearest-neighbor":[100],"(return":[102],"whose":[107],"\u2016\u22c5\u2016_K-distance":[108],"from":[109],"smallest)":[112],"answered":[115],"O^*(n/s^{1/3})":[117],"time;":[118],"all":[119],"k":[120],"homothets":[121],"intersecting":[124],"reported":[128],"additional":[130],"O(k)":[131],"time.":[132,200,226,256],"In":[133],"addition,":[134],"supports":[138],"insertions/deletions":[139],"O^*(s/n)":[141],"amortized":[142],"per":[145],"operation.":[146],"Here":[147],"O^*(\u22c5)":[149],"notation":[150],"hides":[151],"factors":[152],"form":[155],"n^\u03b5,":[156],"where":[157],"\u03b5":[158],">":[159],"0":[160],"arbitrarily":[163],"small":[164],"constant,":[165],"proportionality":[170],"depends":[171],"on":[172,192,236,240],"\u03b5.":[173],"(ii)":[174],"\ud835\udca2(\ud835\udca6)":[176,193],"denote":[177],"intersection":[179],"graph":[180,217,239],"\ud835\udca6.":[182],"Using":[183],"above":[185],"structure,":[187],"breadth-first":[188],"depth-first":[190],"search":[191],"performed":[196,253],"O^*(n^{3/2})":[198,255],"Combining":[201],"this":[202],"result":[203],"with":[204,245],"so-called":[206],"shrink-and-bifurcate":[207],"technique,":[208],"reverse-shortest-path":[210],"problem":[211],"suitably":[214],"defined":[215],"proximity":[216],"solved":[222],"O^*(n^{62/39})":[224],"Dijkstra\u2019s":[227],"shortest-path":[228],"algorithm,":[229,235],"well":[231],"Prim\u2019s":[233],"MST":[234],"\u2016\u22c5\u2016_K-proximity":[238],"points":[242],"edges":[246],"weighted":[247],"by":[248],"\u2016\u22c5\u2016_K,":[249],"also":[251]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-28T00:00:00"}