{"id":"https://openalex.org/W2081442360","doi":"https://doi.org/10.1137/070684483","title":"Efficient Colored Orthogonal Range Counting","display_name":"Efficient Colored Orthogonal Range Counting","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2081442360","doi":"https://doi.org/10.1137/070684483","mag":"2081442360"},"language":"en","primary_location":{"id":"doi:10.1137/070684483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070684483","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"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/A5006699796","display_name":"Haim Kaplan","orcid":"https://orcid.org/0000-0001-9586-8002"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Haim Kaplan","raw_affiliation_strings":["haimk@post.tau.ac.il and rubinnat@post.tau.ac.il and eladv@post.tau.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"haimk@post.tau.ac.il and rubinnat@post.tau.ac.il and eladv@post.tau.ac.il#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014573012","display_name":"Natan Rubin","orcid":"https://orcid.org/0000-0002-7463-6728"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Natan Rubin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["michas@post.tau.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"michas@post.tau.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036740410","display_name":"Elad Verbin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elad Verbin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006699796"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9549,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.95150903,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","issue":"3","first_page":"982","last_page":"1011"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9990000128746033,"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":0.9987999796867371,"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/matrix-multiplication","display_name":"Matrix multiplication","score":0.7198469638824463},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6394643783569336},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6324213743209839},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.6181814074516296},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6105010509490967},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6062150597572327},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5645245313644409},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.49763181805610657},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.496603786945343},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47821494936943054},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.4351568818092346},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4252532124519348},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.421150267124176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25182321667671204}],"concepts":[{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.7198469638824463},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6394643783569336},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6324213743209839},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.6181814074516296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6105010509490967},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6062150597572327},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5645245313644409},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.49763181805610657},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.496603786945343},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47821494936943054},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.4351568818092346},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4252532124519348},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.421150267124176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25182321667671204},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070684483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070684483","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1584486777","https://openalex.org/W1971622590","https://openalex.org/W1979630448","https://openalex.org/W1979740015","https://openalex.org/W1992963068","https://openalex.org/W2005411543","https://openalex.org/W2026204209","https://openalex.org/W2027387410","https://openalex.org/W2033961328","https://openalex.org/W2040746822","https://openalex.org/W2042364367","https://openalex.org/W2043670592","https://openalex.org/W2058127000","https://openalex.org/W2064088517","https://openalex.org/W2070356817","https://openalex.org/W2079176421","https://openalex.org/W2089311600","https://openalex.org/W2125357268","https://openalex.org/W4235042979","https://openalex.org/W4254977685"],"related_works":["https://openalex.org/W3099313426","https://openalex.org/W4287593139","https://openalex.org/W752783541","https://openalex.org/W1506547947","https://openalex.org/W4206811032","https://openalex.org/W2995605830","https://openalex.org/W4239424132","https://openalex.org/W2086123442","https://openalex.org/W2596457687","https://openalex.org/W3212757063"],"abstract_inverted_index":{"Let":[0],"P":[1,27],"be":[2],"a":[3,29,59,67,144,184],"set":[4],"of":[5,18,36,48,51,54,84,153,178],"n":[6],"points":[7,53],"in":[8,125,158,166,197,199],"$\\mathbb{R}^d$,":[9],"so":[10],"that":[11,32,65,94,157,169],"each":[12],"point":[13],"is":[14,77],"colored":[15],"by":[16],"one":[17],"C":[19],"given":[20],"colors.":[21],"We":[22,57,91,106,142],"present":[23,58,108,183],"algorithms":[24],"for":[25,95,111],"preprocessing":[26,127],"into":[28],"data":[30,99],"structure":[31,100],"efficiently":[33],"supports":[34],"queries":[35],"the":[37,46,52,85,98,117,126,150,167,175],"following":[38],"form:":[39],"Given":[40],"an":[41],"axis-parallel":[42],"box":[43],"Q,":[44],"count":[45],"number":[47],"distinct":[49],"colors":[50,196],"$P\\cap":[55],"Q$.":[56],"general":[60],"and":[61,71,189],"relatively":[62],"simple":[63],"solution":[64,120],"has":[66],"polylogarithmic":[68],"query":[69],"time":[70],"worst-case":[72],"storage":[73],"about":[74],"$O(n^d)$.":[75],"It":[76],"based":[78],"on":[79],"several":[80,109],"interesting":[81],"structural":[82],"properties":[83],"problem,":[86,154],"which":[87,137,155],"we":[88,132,182],"establish":[89],"here.":[90],"also":[92],"show":[93,190],"random":[96],"inputs,":[97],"requires":[101],"almost":[102],"linear":[103],"expected":[104],"storage.":[105],"then":[107],"techniques":[110],"achieving":[112],"space-time":[113],"tradeoff.":[114],"In":[115,129],"$\\mathbb{R}^2$,":[116],"most":[118],"efficient":[119],"uses":[121],"fast":[122],"matrix":[123,147,179,186],"multiplication":[124,148,187],"stage.":[128],"higher":[130,200],"dimensions":[131],"use":[133],"simpler":[134],"tradeoff":[135],"mechanisms,":[136],"behave":[138],"just":[139],"as":[140],"well.":[141],"give":[143],"reduction":[145],"from":[146],"to":[149,194],"off-line":[151],"version":[152],"shows":[156],"$\\mathbb{R}^2$":[159],"our":[160],"time-space":[161],"tradeoffs":[162],"are":[163],"reasonably":[164],"sharp,":[165],"sense":[168],"improving":[170],"them":[171],"substantially":[172],"would":[173],"improve":[174],"best":[176],"exponent":[177],"multiplication.":[180],"Finally,":[181],"generalized":[185],"problem":[188],"its":[191],"intimate":[192],"relation":[193],"counting":[195],"boxes":[198],"dimension.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2025-10-10T00:00:00"}