{"id":"https://openalex.org/W2025426553","doi":"https://doi.org/10.1002/(sici)1520-684x(199903)30:3<31::aid-scj4>3.0.co;2-b","title":"Convex hull problem with imprecise input and its solution","display_name":"Convex hull problem with imprecise input and its solution","publication_year":1999,"publication_date":"1999-03-01","ids":{"openalex":"https://openalex.org/W2025426553","doi":"https://doi.org/10.1002/(sici)1520-684x(199903)30:3<31::aid-scj4>3.0.co;2-b","mag":"2025426553"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1520-684x(199903)30:3<31::aid-scj4>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1520-684x(199903)30:3<31::aid-scj4>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S58208175","display_name":"Systems and Computers in Japan","issn_l":"0882-1666","issn":["0882-1666","1520-684X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems and Computers in Japan","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/A5103002593","display_name":"Takayuki Nagai","orcid":null},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Takayuki Nagai","raw_affiliation_strings":["Graduate School of Engineering Science, Osaka University, Osaka, Japan","Graduate school of Engineering Science, Osaka University, Osaka, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering Science, Osaka University, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Graduate school of Engineering Science, Osaka University, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017483433","display_name":"Seigo Yasutome","orcid":null},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Seigo Yasutome","raw_affiliation_strings":["Education Center for Information Processing, Osaka University, Osaka, Japan"],"affiliations":[{"raw_affiliation_string":"Education Center for Information Processing, Osaka University, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112263709","display_name":"Nobuki Tokura","orcid":null},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Nobuki Tokura","raw_affiliation_strings":["Graduate School of Engineering Science, Osaka University, Osaka, Japan","Graduate school of Engineering Science, Osaka University, Osaka, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering Science, Osaka University, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Graduate school of Engineering Science, Osaka University, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103002593"],"corresponding_institution_ids":["https://openalex.org/I98285908"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.13198664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"30","issue":"3","first_page":"31","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9986000061035156,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9907000064849854,"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/convex-hull","display_name":"Convex hull","score":0.9106979370117188},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.8518657088279724},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.584194004535675},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5602519512176514},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5318177938461304},{"id":"https://openalex.org/keywords/output-sensitive-algorithm","display_name":"Output-sensitive algorithm","score":0.5173237323760986},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4917786419391632},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4562593102455139},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4053705930709839},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37069982290267944},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32472479343414307},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2823842167854309},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.24164089560508728},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09665799140930176}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.9106979370117188},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.8518657088279724},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.584194004535675},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5602519512176514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5318177938461304},{"id":"https://openalex.org/C39132409","wikidata":"https://www.wikidata.org/wiki/Q7112860","display_name":"Output-sensitive algorithm","level":5,"score":0.5173237323760986},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4917786419391632},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4562593102455139},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4053705930709839},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37069982290267944},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32472479343414307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2823842167854309},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.24164089560508728},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09665799140930176},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1520-684x(199903)30:3<31::aid-scj4>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1520-684x(199903)30:3<31::aid-scj4>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S58208175","display_name":"Systems and Computers in Japan","issn_l":"0882-1666","issn":["0882-1666","1520-684X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems and Computers in Japan","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1980080397","https://openalex.org/W1998115980","https://openalex.org/W2025299767","https://openalex.org/W2050284373","https://openalex.org/W2082233487","https://openalex.org/W2122026921","https://openalex.org/W2155865801","https://openalex.org/W2165543827","https://openalex.org/W6663058496","https://openalex.org/W6678322375"],"related_works":["https://openalex.org/W1507382935","https://openalex.org/W2358001426","https://openalex.org/W2439874932","https://openalex.org/W1758159897","https://openalex.org/W2360117020","https://openalex.org/W2376690466","https://openalex.org/W2741067195","https://openalex.org/W3034791572","https://openalex.org/W1980352082","https://openalex.org/W1786647412"],"abstract_inverted_index":{"In":[0,59],"computational":[1],"geometry,":[2],"many":[3,28],"implementing":[4],"issues":[5],"have":[6,30],"been":[7,31],"studied":[8,32],"which":[9,106,120,137,152],"arise":[10],"from":[11],"arithmetic":[12,41],"error":[13,57,73,91,169],"or":[14,110,205],"input":[15,56,72,90,168,174],"error.":[16,42],"For":[17,176],"the":[18,48,64,69,79,93,99,102,165],"convex":[19,49,65],"hull":[20,50,66,81],"problem,":[21],"a":[22,53,76,135],"basic":[23],"problem":[24,51,67],"in":[25,52,186,198],"this":[26,60],"field,":[27],"algorithms":[29,151],"concerning":[33],"these":[34],"issues.":[35],"However,":[36],"most":[37],"of":[38,71,104,112,124,141,167],"them":[39,142],"consider":[40,63],"There":[43],"are":[44,107,116],"few":[45],"studies":[46],"on":[47],"situation":[54],"where":[55,78],"exists.":[58],"paper,":[61],"we":[62],"with":[68],"existence":[70],"and":[74,92,134,158,191],"introduce":[75],"method":[77],"output":[80],"is":[82,121,128,138,143,170,184,196],"divided":[83],"into":[84],"two":[85],"parts:":[86],"one":[87],"sensitive":[88],"to":[89,96],"other":[94],"insensitive":[95,100],"it.":[97],"As":[98],"part,":[101],"boundaries":[103],"regions":[105],"always":[108,122,139],"inside":[109,123],"outside":[111,140],"all":[113,125],"possible":[114,126],"hulls":[115,127],"constructed.":[117],"A":[118],"region":[119,136,157,162,183,195],"called":[129,144],"an":[130,145,154,159,180,192],"internal":[131,155,193],"reliable":[132,147,156,161,182,194],"region,":[133],"external":[146,160,181],"region.":[148],"We":[149],"show":[150],"calculate":[153],"assuming":[163],"that":[164],"size":[166],"given":[171,177],"for":[172],"each":[173],"point.":[175],"n":[178],"points,":[179],"calculated":[185,197],"O(n":[187,199],"log":[188,200],"n)":[189,201],"time,":[190],"time":[202,207],"(best":[203],"case),":[204],"O(n3)":[206],"(worst":[208],"case).":[209],"\u00a9":[210],"1999":[211,219],"Scripta":[212],"Technica,":[213],"Syst":[214],"Comp":[215],"Jpn,":[216],"30(3):":[217],"31\u201342,":[218]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}