{"id":"https://openalex.org/W1905058507","doi":"https://doi.org/10.1137/0219065","title":"Sorting Points Along an Algebraic Curve","display_name":"Sorting Points Along an Algebraic Curve","publication_year":1990,"publication_date":"1990-10-01","ids":{"openalex":"https://openalex.org/W1905058507","doi":"https://doi.org/10.1137/0219065","mag":"1905058507"},"language":"en","primary_location":{"id":"doi:10.1137/0219065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0219065","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/A5031591506","display_name":"John K. Johnstone","orcid":"https://orcid.org/0000-0003-4033-0066"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John K. Johnstone","raw_affiliation_strings":["Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":null,"display_name":"Chanderjit L. Bajaj","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chanderjit L. Bajaj","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031591506"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":1.7043,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8254469,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"5","first_page":"925","last_page":"967"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"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":0.9994999766349792,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9966999888420105,"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/curve-fitting","display_name":"Curve fitting","score":0.5203080177307129},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.510618269443512},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.5089795589447021},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.49653202295303345},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.4894653558731079},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4533892273902893},{"id":"https://openalex.org/keywords/tree-traversal","display_name":"Tree traversal","score":0.4361168146133423},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.421726256608963},{"id":"https://openalex.org/keywords/sorting-algorithm","display_name":"Sorting algorithm","score":0.41228818893432617},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38675373792648315},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3362693190574646},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21418362855911255}],"concepts":[{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.5203080177307129},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.510618269443512},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.5089795589447021},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.49653202295303345},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.4894653558731079},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4533892273902893},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.4361168146133423},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.421726256608963},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.41228818893432617},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38675373792648315},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3362693190574646},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21418362855911255},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/0219065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0219065","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:docs.lib.purdue.edu:cstech-1702","is_oa":false,"landing_page_url":"https://docs.lib.purdue.edu/cstech/703","pdf_url":null,"source":{"id":"https://openalex.org/S4377196310","display_name":"Purdue e-Pubs (Purdue University System)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801333002","host_organization_name":"Purdue University System","host_organization_lineage":["https://openalex.org/I2801333002"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Computer Science Technical Reports","raw_type":"text"},{"id":"pmh:oai:ecommons.cornell.edu:1813/6681","is_oa":false,"landing_page_url":"https://hdl.handle.net/1813/6681","pdf_url":null,"source":{"id":"https://openalex.org/S4306400757","display_name":"eCommons (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"technical report"},{"id":"mag:1905058507","is_oa":false,"landing_page_url":"https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1702&context=cstech","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6800000071525574,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W79131202","https://openalex.org/W1514914425","https://openalex.org/W1516027685","https://openalex.org/W1585287174","https://openalex.org/W1801747540","https://openalex.org/W1971842242","https://openalex.org/W1975470983","https://openalex.org/W1983487792","https://openalex.org/W1984346383","https://openalex.org/W1985668290","https://openalex.org/W1994072439","https://openalex.org/W2017794685","https://openalex.org/W2026082049","https://openalex.org/W2035613768","https://openalex.org/W2088864905","https://openalex.org/W2105763874","https://openalex.org/W2126876121","https://openalex.org/W2911302472","https://openalex.org/W3041834803","https://openalex.org/W3217399827","https://openalex.org/W4229917934","https://openalex.org/W4236407746","https://openalex.org/W4246246367"],"related_works":["https://openalex.org/W2017794685","https://openalex.org/W2026082049","https://openalex.org/W2798442789","https://openalex.org/W1977574397","https://openalex.org/W1516027685","https://openalex.org/W2033013465","https://openalex.org/W1523185471","https://openalex.org/W3023760933","https://openalex.org/W1682415012","https://openalex.org/W2077725083","https://openalex.org/W2028788658","https://openalex.org/W2138341573","https://openalex.org/W2027411255","https://openalex.org/W35137244","https://openalex.org/W1970805144","https://openalex.org/W2098458691","https://openalex.org/W2064842799","https://openalex.org/W2778635265","https://openalex.org/W1987582044","https://openalex.org/W1488088034"],"abstract_inverted_index":{"An":[0],"operation":[1],"that":[2,52],"is":[3,14,38,79,123,145],"frequently":[4],"needed":[5],"during":[6],"the":[7,15,36,50,87,142,190],"creation":[8],"and":[9,97,121,147,182],"manipulation":[10],"of":[11,17,27,33,89,127,131,141,150,157,178],"geometric":[12],"models":[13],"sorting":[16,70,152,166],"points":[18,34,71,108,115,173,187],"along":[19,44,64,72],"an":[20,28,110,175,179],"algebraic":[21,29,77,92,112,158,180],"curve.":[22],"Given":[23],"a":[24,31,73,90,155],"segment":[25,177],"$\\overset{\\lower0.5em\\hbox{$\\smash{\\scriptscriptstyle\\frown}$}}{AB}$":[26,45],"curve,":[30],"set":[32],"on":[35,109,154,174,189],"curve":[37,78,93,113,181],"sorted":[39],"from":[40,60],"A":[41,61,66],"to":[42,62,136,171,183],"B":[43,63],"by":[46],"putting":[47],"them":[48],"into":[49,94],"order":[51],"they":[53],"would":[54],"be":[55,169],"encountered":[56],"in":[57,83,100],"traveling":[58],"continuously":[59],"$\\overset{\\lower0.5em\\hbox{$\\smash{\\scriptscriptstyle\\frown}$}}{AB}$.":[65],"new":[67,104,143],"method":[68,85,105,144],"for":[69,165],"plane":[74,91],"or":[75],"space":[76],"presented.":[80,161],"Key":[81],"steps":[82],"this":[84,101],"are":[86,160],"decomposition":[88],"convex":[95],"segments":[96],"point":[98],"location":[99],"decomposition.":[102],"This":[103],"can":[106,167],"sort":[107],"arbitrary":[111,176],"(including":[114],"spread":[116],"over":[117],"several":[118],"connected":[119,192],"components)":[120],"it":[122,134],"particularly":[124],"efficient":[125],"because":[126],"its":[128],"preprocessing,":[129],"both":[130],"which":[132],"make":[133],"superior":[135],"conventional":[137],"methods.":[138],"The":[139,162],"complexity":[140],"analyzed,":[146],"execution":[148],"times":[149],"various":[151],"methods":[153],"number":[156],"curves":[159],"theory":[163],"developed":[164],"also":[168],"used":[170],"locate":[172],"decide":[184],"whether":[185],"two":[186],"lie":[188],"same":[191],"component.":[193]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}