{"id":"https://openalex.org/W1587605567","doi":"https://doi.org/10.1007/s00454-009-9140-z","title":"The Effect of Corners on the Complexity of\u00a0Approximate Range Searching","display_name":"The Effect of Corners on the Complexity of\u00a0Approximate Range Searching","publication_year":2006,"publication_date":"2006-06-05","ids":{"openalex":"https://openalex.org/W1587605567","doi":"https://doi.org/10.1007/s00454-009-9140-z","mag":"1587605567"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-009-9140-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-009-9140-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9140-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9140-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022760571","display_name":"Sunil Arya","orcid":null},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["DE","HK"],"is_corresponding":true,"raw_author_name":"Sunil Arya","raw_affiliation_strings":["The Hong Kong University of Science and Technology","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"The Hong Kong University of Science and Technology","institution_ids":[]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070408072","display_name":"Theocharis Malamatos","orcid":null},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I158716096","display_name":"University of Peloponnese","ror":"https://ror.org/04d4d3c02","country_code":"GR","type":"education","lineage":["https://openalex.org/I158716096"]}],"countries":["DE","GR"],"is_corresponding":false,"raw_author_name":"Theocharis Malamatos","raw_affiliation_strings":["Stadtwald, Saarbr\u00fccken, Germany","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Stadtwald, Saarbr\u00fccken, Germany","institution_ids":[]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016442699","display_name":"David M. Mount","orcid":"https://orcid.org/0000-0002-3290-8932"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David M. Mount","raw_affiliation_strings":["University of Maryland, College Park, Maryland"],"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park, Maryland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022760571"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I200769079"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57078644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"41","issue":"3","first_page":"11","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/range","display_name":"Range (aeronautics)","score":0.5561328530311584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4483998417854309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41705793142318726},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.14196982979774475}],"concepts":[{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5561328530311584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4483998417854309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41705793142318726},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14196982979774475},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":11,"locations":[{"id":"doi:10.1007/s00454-009-9140-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-009-9140-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9140-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"doi:10.1145/1137856.1137860","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1137856.1137860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-second annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.147.5416","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.147.5416","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umd.edu/users/mount/Papers/dcg09-corners.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.407.2492","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.407.2492","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://pelopas.uop.gr/~tmalamat/Papers/Sharp08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.1265","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.1265","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umd.edu/users/mount/Papers/avd-sharp-socg06.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.9411","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.9411","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ust.hk/faculty/arya/pub/corners.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:314541","is_oa":false,"landing_page_url":"http://edoc.mpg.de/314541","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 22nd Annual Symposium on Computational Geometry, SCG'06, ACM, 11-20 (2006)","raw_type":"Conference-Paper"},{"id":"pmh:oai:pure.mpg.de:item_1328566","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-241D-C","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 22nd Annual Symposium on Computational Geometry, SCG'06","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-19364","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-19364","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference paper"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-35635","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-35635","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"mag:1587605567","is_oa":false,"landing_page_url":"http://pubman.mpdl.mpg.de/pubman/item/escidoc:1328566","pdf_url":null,"source":{"id":"https://openalex.org/S4306533943","display_name":"Untitled Event","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Untitled Event","raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s00454-009-9140-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-009-9140-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9140-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2811237814","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G3024094262","display_name":null,"funder_award_id":"N00014-08-1-1015","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4154686922","display_name":null,"funder_award_id":"N00014-08-1-1015","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7869328032","display_name":null,"funder_award_id":"CCR-0635099","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8371110557","display_name":"Approximation Algorithms for Geometric Retrieval","funder_award_id":"0635099","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320323537","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1587605567.pdf","grobid_xml":"https://content.openalex.org/works/W1587605567.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W15475540","https://openalex.org/W1547238168","https://openalex.org/W1553172454","https://openalex.org/W1973949696","https://openalex.org/W1980228393","https://openalex.org/W1995232397","https://openalex.org/W2027387410","https://openalex.org/W2038636610","https://openalex.org/W2046116152","https://openalex.org/W2067636581","https://openalex.org/W2070228513","https://openalex.org/W2078939351","https://openalex.org/W2100440346","https://openalex.org/W2101886696","https://openalex.org/W2115964316","https://openalex.org/W2165576953","https://openalex.org/W2220451813","https://openalex.org/W2738786117","https://openalex.org/W4206206918","https://openalex.org/W6631045115","https://openalex.org/W6652723978"],"related_works":["https://openalex.org/W1992733333","https://openalex.org/W2147578409","https://openalex.org/W1995605359","https://openalex.org/W2147934418","https://openalex.org/W2142984475","https://openalex.org/W1838101748","https://openalex.org/W2912703870","https://openalex.org/W1897841194","https://openalex.org/W1544463887","https://openalex.org/W1977957682","https://openalex.org/W1556860842","https://openalex.org/W2107731443","https://openalex.org/W2068252235","https://openalex.org/W2293207594","https://openalex.org/W1517917152","https://openalex.org/W2043498431","https://openalex.org/W2141882063","https://openalex.org/W2097786134","https://openalex.org/W2152911085","https://openalex.org/W2090032031"],"abstract_inverted_index":{"Given":[0],"an":[1,189,303],"n-element":[2],"point":[3,300],"set":[4],"in":[5,154,212,336,362],"\u211d":[6],"d":[7],",":[8],"the":[9,19,26,30,54,61,73,87,97,120,134,157,193,196,205,213,238,248,278,311,318,363],"range":[10,37,45,91,100,140,210,293,312,331],"searching":[11,46,92,141,211],"problem":[12],"involves":[13],"preprocessing":[14],"these":[15,167],"points":[16,31,62,74],"so":[17],"that":[18,49,63,133,229,277,291,307,323,346],"total":[20],"weight,":[21],"or":[22],"for":[23,109,117,145,151,217,230,270,324],"our":[24],"purposes":[25],"semigroup":[27,98,103,214],"sum,":[28],"of":[29,72,79,89,96,137,156,175,195,208,220,250,259,356,369],"lying":[32,75],"within":[33,65,76,310],"a":[34,255,292,353],"given":[35],"query":[36,239],"\u03b7":[38,50,66],"can":[39,169,333],"be":[40,170,334],"determined":[41],"quickly.":[42],"In":[43,82,161,198,247,273],"\u03b5-approximate":[44,330],"we":[47,85,164,200,253,275],"assume":[48],"is":[51,56,105,114,124,142,150,241,294,302,315,348,361],"bounded,":[52],"and":[53,67,99,112,235,327,366],"sum":[55,122],"required":[57],"to":[58,127,172,285,317],"include":[59,70],"all":[60,110,118],"lie":[64],"may":[68],"additionally":[69],"any":[71],"distance":[77],"\u03b5\u22c5diam(\u03b7)":[78],"\u03b7\u2019s":[80],"boundary.":[81],"this":[83,162,347],"paper":[84,163],"contrast":[86],"complexity":[88,136,194,207],"approximate":[90,138,209],"based":[93],"on":[94,159,186,192,204],"properties":[95],"space.":[101,343,370],"A":[102],"(S,+)":[104],"idempotent":[106,146,328],"if":[107,116,296],"x+x=x":[108],"x\u2208S,":[111],"it":[113,149],"integral":[115,152,251],"k\u22652,":[119],"k-fold":[121],"x+\u22c5\u22c5\u22c5+x":[123],"not":[125],"equal":[126],"x.":[128],"Recent":[129],"research":[130],"has":[131,188],"shown":[132],"computational":[135],"spherical":[139],"significantly":[143],"lower":[144,202,257,263,354],"semigroups":[147,153,234,252],"than":[148],"terms":[155],"dependencies":[158],"\u03b5.":[160],"consider":[165],"whether":[166],"results":[168],"generalized":[171],"other":[173],"sorts":[174],"ranges.":[176,288],"We":[177,227,289,321,344],"show":[178,228,276,322,345],"that,":[179],"as":[180],"with":[181],"integrality,":[182],"allowing":[183],"sharp":[184],"corners":[185],"ranges":[187,218,326],"adverse":[190],"effect":[191],"problem.":[197],"particular,":[199],"establish":[201],"bounds":[203,264,269],"worst-case":[206],"arithmetic":[215],"model":[216,365],"consisting":[219],"d-dimensional":[221],"unit":[222],"hypercubes":[223],"under":[224],"rigid":[225],"motions.":[226],"arbitrary":[231,271],"(including":[232],"idempotent)":[233],"linear":[236],"space,":[237],"time":[240,340],"at":[242,297],"least":[243],"$\\varOmega(1/{\\varepsilon":[244],"}^{d-2\\sqrt{d}})$":[245],".":[246],"case":[249],"prove":[254],"tighter":[256],"bound":[258,355,360],"\u03a9(1/\u03b5":[260],"d\u22122).":[261],"These":[262],"nearly":[265,349],"match":[266],"existing":[267],"upper":[268],"semigroups.":[272],"contrast,":[274],"improvements":[279],"offered":[280],"by":[281,351],"idempotence":[282],"do":[283],"apply":[284],"smooth":[286,295,325],"convex":[287],"say":[290],"every":[298],"boundary":[299],"there":[301],"incident":[304],"Euclidean":[305],"sphere":[306],"lies":[308],"entirely":[309],"whose":[313],"radius":[314],"proportional":[316],"range\u2019s":[319],"diameter.":[320],"semigroups,":[329],"queries":[332],"answered":[335],"O(log":[337],"n+(1/\u03b5)(d\u22121)/2log":[338],"(1/\u03b5))":[339],"using":[341],"O(n/\u03b5)":[342],"tight":[350],"presenting":[352],"\u03a9(log":[357],"n+(1/\u03b5)(d\u22121)/2).":[358],"This":[359],"decision-tree":[364],"holds":[367],"irrespective":[368]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}
