{"id":"https://openalex.org/W2160775966","doi":"https://doi.org/10.1137/s0097539798349188","title":"Random Sampling, Halfspace Range Reporting, and Construction of \\lowercase$(\\le k)$-Levels in Three Dimensions","display_name":"Random Sampling, Halfspace Range Reporting, and Construction of \\lowercase$(\\le k)$-Levels in Three Dimensions","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2160775966","doi":"https://doi.org/10.1137/s0097539798349188","mag":"2160775966"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539798349188","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032955418","display_name":"Timothy M. Chan","orcid":"https://orcid.org/0000-0002-8093-0675"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Timothy M. Chan","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5032955418"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.733,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":89,"citation_normalized_percentile":{"value":0.987852,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"30","issue":"2","first_page":"561","last_page":"575"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9999,"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":0.9999,"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":0.9977,"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":0.9975,"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/log-log-plot","display_name":"Log-log plot","score":0.52237064},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized Algorithm","score":0.47641194}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.77904207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.692353},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.678534},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6150174},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6148374},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.52237064},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.49314898},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.47641194},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.44990617},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42031634},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3491636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3377441},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15425354},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14851898},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539798349188","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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":36,"referenced_works":["https://openalex.org/W1847031659","https://openalex.org/W1965146563","https://openalex.org/W1967005434","https://openalex.org/W1974821267","https://openalex.org/W1986004959","https://openalex.org/W1989130580","https://openalex.org/W1996570135","https://openalex.org/W2005807476","https://openalex.org/W2006769458","https://openalex.org/W2012504811","https://openalex.org/W2016400774","https://openalex.org/W2032966476","https://openalex.org/W2039849774","https://openalex.org/W2041775009","https://openalex.org/W2048493433","https://openalex.org/W2048729985","https://openalex.org/W2050459520","https://openalex.org/W2052948190","https://openalex.org/W2060978628","https://openalex.org/W2061845601","https://openalex.org/W2067631433","https://openalex.org/W2070747743","https://openalex.org/W2071676345","https://openalex.org/W2074863496","https://openalex.org/W2079093471","https://openalex.org/W2094650250","https://openalex.org/W2103777374","https://openalex.org/W2103893986","https://openalex.org/W2120934134","https://openalex.org/W2127371054","https://openalex.org/W2136963423","https://openalex.org/W2147950904","https://openalex.org/W2168352426","https://openalex.org/W4235042979","https://openalex.org/W4254977685","https://openalex.org/W4300640952"],"related_works":["https://openalex.org/W4377371889","https://openalex.org/W2565109825","https://openalex.org/W2113623403","https://openalex.org/W2055932080","https://openalex.org/W2036758175","https://openalex.org/W2018076478","https://openalex.org/W2011106535","https://openalex.org/W1994598067","https://openalex.org/W1992470151","https://openalex.org/W1541068124"],"abstract_inverted_index":{"Given":[0],"n":[1,60],"points":[2],"in":[3,15,31,56,62,68,83,105],"three":[4,63],"dimensions,":[5],"we":[6],"show":[7],"how":[8],"to":[9,42],"answer":[10],"halfspace":[11],"range":[12],"reporting":[13],"queries":[14,95],"O(log":[16],"n+k)":[17],"expected":[18,36,73,111],"time":[19],"for":[20,49,91],"an":[21,57,87,97],"output":[22],"size":[23],"k.":[24],"Our":[25,75],"data":[26,89],"structure":[27,90],"can":[28],"be":[29],"preprocessed":[30],"optimal":[32,46],"O(n":[33,69,106],"log":[34,70,107,109],"n)":[35],"time.":[37,74,112],"We":[38],"apply":[39],"this":[40],"result":[41],"obtain":[43],"the":[44,50,53,101],"first":[45],"randomized":[47],"algorithm":[48,66,98],"construction":[51],"of":[52,59],"$(\\le":[54],"k)$-level":[55],"arrangement":[58],"planes":[61],"dimensions.":[64],"The":[65],"runs":[67],"n+nk2":[71],")":[72],"techniques":[76],"are":[77],"based":[78],"on":[79],"random":[80],"sampling.":[81],"Applications":[82],"two":[84],"dimensions":[85],"include":[86],"improved":[88],"\"k":[92],"nearest":[93],"neighbors\"":[94],"and":[96],"that":[99],"constructs":[100],"order-k":[102],"Voronoi":[103],"diagram":[104],"n+nk":[108],"k)":[110]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2160775966","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2024-12-08T02:37:03.430373","created_date":"2016-06-24"}