{"id":"https://openalex.org/W2078001727","doi":"https://doi.org/10.1137/120900708","title":"Computing Correlation between Piecewise-Linear Functions","display_name":"Computing Correlation between Piecewise-Linear Functions","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2078001727","doi":"https://doi.org/10.1137/120900708","mag":"2078001727"},"language":"en","primary_location":{"id":"doi:10.1137/120900708","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120900708","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2117/23696","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058649592","display_name":"Pankaj K. Agarwal","orcid":"https://orcid.org/0000-0002-9439-181X"},"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":true,"raw_author_name":"Pankaj K. Agarwal","raw_affiliation_strings":["Duke University"],"affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042232059","display_name":"Boris Aronov","orcid":"https://orcid.org/0000-0003-3110-4702"},"institutions":[{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Boris Aronov","raw_affiliation_strings":["Polytechnic Institute of New York University"],"affiliations":[{"raw_affiliation_string":"Polytechnic Institute of New York University","institution_ids":["https://openalex.org/I90965887","https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053874521","display_name":"Marc van Kreveld","orcid":"https://orcid.org/0000-0001-8208-3468"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Marc van Kreveld","raw_affiliation_strings":["Utrecht university >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Utrecht university >  >  >  >","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112038936","display_name":"Maarten L\u00f6ffler","orcid":null},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Maarten L\u00f6ffler","raw_affiliation_strings":["Utrecht university >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Utrecht university >  >  >  >","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074443763","display_name":"Rodrigo I. Silveira","orcid":"https://orcid.org/0000-0003-0202-4543"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rodrigo I. Silveira","raw_affiliation_strings":["Polytechnic University of Catalonia"],"affiliations":[{"raw_affiliation_string":"Polytechnic University of Catalonia","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5058649592"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":1.4007,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.85211158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"42","issue":"5","first_page":"1867","last_page":"1887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9987999796867371,"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":0.9915000200271606,"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/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5401502847671509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5359170436859131},{"id":"https://openalex.org/keywords/correlation","display_name":"Correlation","score":0.5270932912826538},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32575446367263794},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14561474323272705}],"concepts":[{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5401502847671509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5359170436859131},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.5270932912826538},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32575446367263794},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14561474323272705},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/120900708","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120900708","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"},{"id":"pmh:oai:upcommons.upc.edu:2117/23696","is_oa":false,"landing_page_url":"https://hdl.handle.net/2117/23696","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.recercat.cat:2072/238529","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/23696","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.406.7603","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.7603","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.duke.edu/~pankaj/publications/papers/terr-sim.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:www.recercat.cat:2072/238529","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/23696","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1566404621","https://openalex.org/W1571356903","https://openalex.org/W1973475129","https://openalex.org/W1987752344","https://openalex.org/W1988106539","https://openalex.org/W2008434505","https://openalex.org/W2028747718","https://openalex.org/W2059155916","https://openalex.org/W2059571566","https://openalex.org/W2063346183","https://openalex.org/W2068141203","https://openalex.org/W2068769655","https://openalex.org/W2100306205","https://openalex.org/W2102501784","https://openalex.org/W2113830395","https://openalex.org/W2126231666","https://openalex.org/W2127752113","https://openalex.org/W2128831569","https://openalex.org/W2143022286","https://openalex.org/W2163727044","https://openalex.org/W2167816765","https://openalex.org/W4206206918","https://openalex.org/W4232425010"],"related_works":["https://openalex.org/W2322438548","https://openalex.org/W1994574086","https://openalex.org/W4242276272","https://openalex.org/W4240768513","https://openalex.org/W2086023871","https://openalex.org/W2031007207","https://openalex.org/W4230698634","https://openalex.org/W2076919693","https://openalex.org/W2754997651","https://openalex.org/W2033511865"],"abstract_inverted_index":{"We":[0,40,86],"study":[1],"the":[2,18,34,47,52,55,65,74,80,83,93,97,143,149],"problem":[3],"of":[4,33,54,62,64,77,82,99,152],"computing":[5],"correlation":[6],"between":[7,51,96],"two":[8,56,84,144],"piecewise-linear":[9],"bivariate":[10,102,131],"functions":[11,106,132,145],"defined":[12,147],"over":[13,58,148],"a":[14,30,42,109],"common":[15],"domain,":[16],"where":[17,71],"surfaces":[19],"they":[20],"define":[21],"in":[22,67,79,114,134],"three":[23],"dimensions---polyhedral":[24],"terrains---can":[25],"be":[26],"transformed":[27],"vertically":[28],"by":[29],"linear":[31,60],"transformation":[32],"third":[35],"coordinate":[36],"(scaling":[37],"and":[38,101],"translation).":[39],"present":[41,88,108],"randomized":[43],"algorithm":[44,111,129],"that":[45,112],"minimizes":[46],"maximum":[48],"vertical":[49],"distance":[50,95],"graphs":[53,81,98],"functions,":[57],"all":[59],"transformations":[61],"one":[63],"terrains,":[66],"$O(n^{4/3}\\operatorname{polylog}n)$":[68],"expected":[69,120],"time,":[70,136],"$n$":[72],"is":[73],"total":[75],"number":[76],"vertices":[78],"functions.":[85,103],"also":[87],"approximation":[89],"algorithms":[90],"for":[91,122,130,137],"minimizing":[92],"mean":[94],"univariate":[100,105],"For":[104],"we":[107],"$(1+\\varepsilon)$-approximation":[110,128],"runs":[113,133],"$O(n":[115],"(1":[116],"+":[117],"\\log^2":[118],"(1/\\varepsilon)))$":[119],"time":[121],"any":[123,138],"fixed":[124,139],"$\\varepsilon":[125,140],">0$.":[126],"The":[127],"$O(n/\\varepsilon)$":[135],">0$,":[141],"provided":[142],"are":[146],"same":[150],"triangulation":[151],"their":[153],"domain.":[154]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}