{"id":"https://openalex.org/W1588671849","doi":"https://doi.org/10.1142/s0218195997000260","title":"The Rectangle Enclosure and Point-Dominance Problems Revisited","display_name":"The Rectangle Enclosure and Point-Dominance Problems Revisited","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1588671849","doi":"https://doi.org/10.1142/s0218195997000260","mag":"1588671849"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195997000260","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195997000260","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/220279.220297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102100978","display_name":"Prosenjit Gupta","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"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"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Prosenjit Gupta","raw_affiliation_strings":["Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, USA","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"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/A5050894676","display_name":"Ravi Janardan","orcid":"https://orcid.org/0000-0003-3922-6763"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ravi Janardan","raw_affiliation_strings":["Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108374265","display_name":"Michiel Smid","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/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michiel Smid","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, D-66123 Saarbr\u00fccken, Germany","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, D-66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":null,"display_name":"Bhaskar Dasgupta","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bhaskar Dasgupta","raw_affiliation_strings":["Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.01,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69551935,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"07","issue":"05","first_page":"162","last_page":"171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.972100019454956,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.972100019454956,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9071999788284302,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/enclosure","display_name":"Enclosure","score":0.8969713449478149},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.57893967628479},{"id":"https://openalex.org/keywords/dominance","display_name":"Dominance (genetics)","score":0.5531976819038391},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45652902126312256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3994693458080292},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3093826174736023},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20935535430908203},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.13104739785194397},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.05740663409233093}],"concepts":[{"id":"https://openalex.org/C98375054","wikidata":"https://www.wikidata.org/wiki/Q442709","display_name":"Enclosure","level":2,"score":0.8969713449478149},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.57893967628479},{"id":"https://openalex.org/C151913843","wikidata":"https://www.wikidata.org/wiki/Q3454555","display_name":"Dominance (genetics)","level":3,"score":0.5531976819038391},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45652902126312256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3994693458080292},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3093826174736023},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20935535430908203},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.13104739785194397},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.05740663409233093},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":14,"locations":[{"id":"doi:10.1142/s0218195997000260","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195997000260","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"},{"id":"doi:10.1145/220279.220297","is_oa":true,"landing_page_url":"https://doi.org/10.1145/220279.220297","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/220279.220297","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the eleventh annual symposium on Computational geometry - SCG '95","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.mpg.de:item_1834233","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-B525-8","pdf_url":"https://pure.mpg.de/pubman/item/item_1834233_2/component/file_1857841/MPI-I-94-142.pdf","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Report / Max-Planck-Institut f\u00fcr Informatik","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.391","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.391","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.mpi-sb.mpg.de/pub/papers/reports/MPI-I-94-142.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.52.9976","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.9976","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://crab.rutgers.edu/~bhaskar/resume/publ/papers/cg95pap.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.56.2156","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.2156","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://crab.rutgers.edu/~bhaskar/resume/publ/papers/final-paper.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.74.7168","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.74.7168","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://crab.rutgers.edu/~bhaskar/resume/publ/papers/final-paper.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:517753","is_oa":false,"landing_page_url":"http://edoc.mpg.de/517753","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":"11th Annual ACM Symposium on Computing Geometry, -, 162-171 (1995)","raw_type":"Conference-Paper"},{"id":"pmh:oai:edoc.mpg.de:517883","is_oa":false,"landing_page_url":"http://edoc.mpg.de/517883","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":"11th Annual !CM Symposium on Computational Geometry, acm-Press, 162-171 (1995)","raw_type":"Conference-Paper"},{"id":"pmh:oai:edoc.mpg.de:517919","is_oa":false,"landing_page_url":"http://edoc.mpg.de/517919","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":"International Journal of Computational Geometry and Applications, v.7, 437-456 (1997)","raw_type":"Article"},{"id":"pmh:oai:pure.mpg.de:item_1331591","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-39B8-3","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":"International Journal of Computational Geometry and Applications","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.mpg.de:item_1331880","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-ACD9-E","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 11th Annual ACM Symposium on Computing Geometry","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:pure.mpg.de:item_1331881","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-ACDB-A","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":"11th Annual !CM Symposium on Computational Geometry","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"mag:1588671849","is_oa":false,"landing_page_url":"http://pubman.mpdl.mpg.de/pubman/item/escidoc:1331881","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:10.1145/220279.220297","is_oa":true,"landing_page_url":"https://doi.org/10.1145/220279.220297","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/220279.220297","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the eleventh annual symposium on Computational geometry - SCG '95","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1588671849.pdf","grobid_xml":"https://content.openalex.org/works/W1588671849.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2064303129"],"related_works":[],"abstract_inverted_index":{"We":[0,174,204],"consider":[1,224],"the":[2,6,61,69,122,126,134,154,160,163,186,212,225,229,243],"problem":[3,170,181],"of":[4,12,30,63,71,129,159,189,192,201,236],"reporting":[5,24,169],"pairwise":[7],"enclosures":[8],"in":[9,16,27,33,99,215,245,256],"a":[10,28,38,75,118,166,176,190,232],"set":[11,29],"n":[13,31,49,102,105,258,260],"axes-parallel":[14],"rectangles":[15,230],"\u211d":[17,34],"2":[18],",":[19],"which":[20,91,182,219,240,254],"is":[21,60,74,116,151,162,183,220,241],"equivalent":[22],"to":[23,140,165],"dominance":[25,168],"pairs":[26],"points":[32],"4":[35],".":[36],"Over":[37],"decade":[39],"ago,":[40],"Lee":[41],"and":[42,52,97,264],"Preparata":[43],"7":[44],"gave":[45],"an":[46,80,89,252],"O(n":[47,93,100],"log":[48,101,103,104,108,109,259],"+":[50,94,106,261],"k)-time":[51],"O(n)-space":[53],"algorithm":[54,77,90,124,150,161,208,253],"for":[55,125,179],"these":[56],"problems,":[57],"where":[58,228],"k":[59,107],"number":[62],"reported":[64],"pairs.":[65],"Since":[66],"that":[67],"time,":[68],"question":[70],"whether":[72],"there":[73],"faster":[76],"has":[78],"remained":[79],"intriguing":[81],"open":[82,147],"problem.":[83,148],"In":[84],"this":[85,145,180,248],"paper,":[86],"we":[87,223,250],"give":[88,175,251],"uses":[92,265],"k)":[95,262],"space":[96],"runs":[98,255],"n)":[110],"time.":[111],"Thus,":[112],"although":[113],"our":[114],"result":[115,136],"not":[117],"strict":[119],"improvement":[120],"over":[121],"Lee-Preparata":[123],"full":[127],"range":[128],"k,":[130],"it":[131],"is,":[132],"nevertheless,":[133],"first":[135],"since":[137],"Ref.":[138,216],"(6)":[139],"make":[141],"any":[142],"progress":[143],"on":[144,153,185],"long-standing":[146],"Our":[149],"based":[152,184],"divide-and-conquer":[155],"paradigm.":[156],"The":[157],"heart":[158],"solution":[164,178,197],"red-blue":[167],"(the":[171],"\"merge\"":[172],"step).":[173],"novel":[177],"iterative":[187],"application":[188],"sequence":[191],"non-trivial":[193],"sweep":[194],"routines.":[195],"This":[196],"technique":[198],"should":[199],"be":[200],"independent":[202],"interest.":[203],"also":[205],"present":[206],"another":[207],"whose":[209],"bounds":[210,213],"match":[211],"given":[214],"(6),":[217],"but":[218],"simpler.":[221],"Finally,":[222],"special":[226],"case":[227,244],"have":[231],"small":[233],"number,":[234],"\u03b1,":[235],"different":[237],"aspect":[238],"ratios,":[239],"often":[242],"practice.":[246],"For":[247],"problem,":[249],"O(\u03b1":[257],"time":[263],"O(n)":[266],"space.":[267]},"counts_by_year":[],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}