{"id":"https://openalex.org/W2037058319","doi":"https://doi.org/10.1137/090769077","title":"A Linear Time Algorithm for Near Minimax Continuous Piecewise Linear Representations of Discrete Data","display_name":"A Linear Time Algorithm for Near Minimax Continuous Piecewise Linear Representations of Discrete Data","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2037058319","doi":"https://doi.org/10.1137/090769077","mag":"2037058319"},"language":"en","primary_location":{"id":"doi:10.1137/090769077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090769077","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10214/6589","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025828965","display_name":"Emily K. Szusz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emily K. Szusz","raw_affiliation_strings":["eszusz@uoguelph.ca and AWillms@uoguelph.ca#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"eszusz@uoguelph.ca and AWillms@uoguelph.ca#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090963780","display_name":"Allan R. Willms","orcid":"https://orcid.org/0000-0003-3502-5163"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Allan R. Willms","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3336,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67480459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"5","first_page":"2584","last_page":"2602"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.994700014591217,"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"}},"topics":[{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.994700014591217,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9817000031471252,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7513713836669922},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6302900910377502},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.5802821516990662},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5521659255027771},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5379126667976379},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5202547311782837},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.49722030758857727},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4965437054634094},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.48516422510147095},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.42243319749832153},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.41856762766838074},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.315115749835968},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17747551202774048},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17268869280815125},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.1038762629032135}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7513713836669922},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6302900910377502},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.5802821516990662},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5521659255027771},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5379126667976379},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5202547311782837},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.49722030758857727},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4965437054634094},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.48516422510147095},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42243319749832153},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.41856762766838074},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.315115749835968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17747551202774048},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17268869280815125},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.1038762629032135},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090769077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090769077","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.991.8852","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.991.8852","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://atrium.lib.uoguelph.ca/xmlui/bitstream/handle/10214/6589/Szusz_Willms_SIAMJSciComput_2010.pdf%3Bjsessionid%3DABE6FAC0BB94A1F53B63957875147935?sequence%3D1","raw_type":"text"},{"id":"pmh:oai:atrium.lib.uoguelph.ca:10214/6589","is_oa":true,"landing_page_url":"http://hdl.handle.net/10214/6589","pdf_url":null,"source":{"id":"https://openalex.org/S4306401043","display_name":"The Atrium (University of Guelph)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79817857","host_organization_name":"University of Guelph","host_organization_lineage":["https://openalex.org/I79817857"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:atrium.lib.uoguelph.ca:10214/6589","is_oa":true,"landing_page_url":"http://hdl.handle.net/10214/6589","pdf_url":null,"source":{"id":"https://openalex.org/S4306401043","display_name":"The Atrium (University of Guelph)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79817857","host_organization_name":"University of Guelph","host_organization_lineage":["https://openalex.org/I79817857"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1974434931","https://openalex.org/W1975946664","https://openalex.org/W1981425894","https://openalex.org/W1981934656","https://openalex.org/W1982013156","https://openalex.org/W1993527278","https://openalex.org/W1994833872","https://openalex.org/W2017382275","https://openalex.org/W2022691322","https://openalex.org/W2031435600","https://openalex.org/W2043735243","https://openalex.org/W2058775467","https://openalex.org/W2064497989","https://openalex.org/W2065916793","https://openalex.org/W2072543763","https://openalex.org/W2088876556","https://openalex.org/W2100645164","https://openalex.org/W2102614976","https://openalex.org/W2103429022","https://openalex.org/W2115366404","https://openalex.org/W2140628095","https://openalex.org/W2143702666","https://openalex.org/W2155195832","https://openalex.org/W2170697148","https://openalex.org/W2314485382","https://openalex.org/W2551090992","https://openalex.org/W3105039087"],"related_works":["https://openalex.org/W2953303953","https://openalex.org/W2133947431","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2100864966","https://openalex.org/W2109304297","https://openalex.org/W2083709218","https://openalex.org/W2379261728"],"abstract_inverted_index":{"An":[0],"algorithm":[1,25,137],"that":[2,114],"constructs":[3],"a":[4,11,17,68,74,104,116],"continuous":[5,128],"piecewise":[6],"linear":[7],"representation,":[8,32],"subject":[9,33],"to":[10,34],"certain":[12],"slope/segment":[13],"length":[14],"constraint,":[15,36],"of":[16,20,54,61,91,106,130,141],"given":[18],"set":[19],"data":[21,55,93,121],"is":[22,51,65,110,138],"described.":[23],"The":[24,63,136],"yields":[26],"an":[27],"optimal":[28,31],"or":[29],"near":[30],"this":[35],"in":[37,44],"the":[38,52,59,78,88,92,95,100,120],"$L_{\\infty}$":[39],"norm":[40],"and":[41,57,97,102,123,127,146],"does":[42],"so":[43],"at":[45],"worst":[46],"$O(nK)$":[47],"time,":[48],"where":[49],"n":[50],"number":[53,60],"points":[56],"K":[58],"segments.":[62],"constraint":[64],"determined":[66],"by":[67],"user-specified":[69],"parameter,":[70],"$t_{\\min}$,":[71],"which":[72],"dictates":[73],"lower":[75],"bound":[76],"for":[77,112,119],"distance":[79],"between":[80,132],"opposite-sign":[81],"slope":[82],"discontinuities.":[83],"For":[84],"reasonable":[85],"$t_{\\min}$":[86],"values,":[87],"resulting":[89],"representation":[90,109],"captures":[94],"signal":[96],"both":[98],"smooths":[99],"noise":[101],"provides":[103],"measure":[105],"it.":[107],"This":[108],"useful":[111],"applications":[113],"require":[115],"specified":[117],"interval":[118],"values":[122],"also":[124],"allows":[125],"easy":[126],"interpolation":[129],"ranges":[131],"recorded":[133],"time":[134],"points.":[135],"described,":[139],"some":[140],"its":[142,147],"properties":[143],"are":[144,154],"proven,":[145],"capabilities":[148],"demonstrated":[149],"with":[150,156],"several":[151],"examples.":[152],"Comparisons":[153],"made":[155],"alternative":[157],"techniques.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-31T07:19:18.363097","created_date":"2025-10-10T00:00:00"}