{"id":"https://openalex.org/W2018318565","doi":"https://doi.org/10.1016/0925-7721(95)00036-4","title":"Fast randomized parallel methods for planar convex hull construction","display_name":"Fast randomized parallel methods for planar convex hull construction","publication_year":1997,"publication_date":"1997-03-01","ids":{"openalex":"https://openalex.org/W2018318565","doi":"https://doi.org/10.1016/0925-7721(95)00036-4","mag":"2018318565"},"language":"en","primary_location":{"id":"doi:10.1016/0925-7721(95)00036-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00036-4","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/0925-7721(95)00036-4","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075832239","display_name":"Mujtaba R. Ghouse","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mujtaba R. Ghouse","raw_affiliation_strings":["Quintus Corporation, 301 E. Evelyn Ave., Mountain View, CA 94041, USA"],"affiliations":[{"raw_affiliation_string":"Quintus Corporation, 301 E. Evelyn Ave., Mountain View, CA 94041, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034971300","display_name":"Michael T. Goodrich","orcid":"https://orcid.org/0000-0002-8943-191X"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael T. Goodrich","raw_affiliation_strings":["Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218-2694, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218-2694, USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034971300"],"corresponding_institution_ids":["https://openalex.org/I145311948"],"apc_list":{"value":2180,"currency":"USD","value_usd":2180},"apc_paid":{"value":2180,"currency":"USD","value_usd":2180},"fwci":0.3645,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61949339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","issue":"4","first_page":"219","last_page":"235"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/convex-hull","display_name":"Convex hull","score":0.8906427621841431},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.7728366851806641},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7569013833999634},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6664263606071472},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6624348759651184},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5952126979827881},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.5586063861846924},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5572399497032166},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5280882716178894},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.48188620805740356},{"id":"https://openalex.org/keywords/output-sensitive-algorithm","display_name":"Output-sensitive algorithm","score":0.467949777841568},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38604986667633057},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2497364580631256},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.18270975351333618},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1665075421333313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16458478569984436},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.052962422370910645}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8906427621841431},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.7728366851806641},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7569013833999634},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6664263606071472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6624348759651184},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5952126979827881},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.5586063861846924},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5572399497032166},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5280882716178894},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.48188620805740356},{"id":"https://openalex.org/C39132409","wikidata":"https://www.wikidata.org/wiki/Q7112860","display_name":"Output-sensitive algorithm","level":5,"score":0.467949777841568},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38604986667633057},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2497364580631256},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.18270975351333618},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1665075421333313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16458478569984436},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.052962422370910645},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0925-7721(95)00036-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00036-4","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.47.3360","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.3360","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.jhu.edu/~goodrich/cgc/pubs/inplace.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/0925-7721(95)00036-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00036-4","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1534829670","https://openalex.org/W1975510415","https://openalex.org/W1976915153","https://openalex.org/W1987576325","https://openalex.org/W1996765291","https://openalex.org/W1997347990","https://openalex.org/W1999230788","https://openalex.org/W2000050422","https://openalex.org/W2003583528","https://openalex.org/W2005314985","https://openalex.org/W2011573873","https://openalex.org/W2016482138","https://openalex.org/W2022266599","https://openalex.org/W2025299767","https://openalex.org/W2042587503","https://openalex.org/W2042607215","https://openalex.org/W2057399436","https://openalex.org/W2060690113","https://openalex.org/W2062679636","https://openalex.org/W2077366959","https://openalex.org/W2094855951","https://openalex.org/W2099765347","https://openalex.org/W2104304525","https://openalex.org/W2105778456","https://openalex.org/W2120490947","https://openalex.org/W2129879687","https://openalex.org/W2134921847","https://openalex.org/W3041834803","https://openalex.org/W3048145607","https://openalex.org/W4300640952","https://openalex.org/W6632175332","https://openalex.org/W6647111265","https://openalex.org/W6653362784","https://openalex.org/W6658587526","https://openalex.org/W6665722934","https://openalex.org/W6669621126","https://openalex.org/W6845151110"],"related_works":["https://openalex.org/W2358001426","https://openalex.org/W1507382935","https://openalex.org/W2439874932","https://openalex.org/W2104304525","https://openalex.org/W1758159897","https://openalex.org/W981962503","https://openalex.org/W2360117020","https://openalex.org/W2376690466","https://openalex.org/W2793611696","https://openalex.org/W2741067195"],"abstract_inverted_index":{"We":[0,57],"present":[1],"a":[2,14,124,148],"number":[3,87],"of":[4,27,66,88,113,126],"efficient":[5],"parallel":[6,150],"algorithms":[7],"for":[8,106],"constructing":[9],"2-dimensional":[10],"convex":[11,25,64,92],"hulls":[12],"on":[13,110,123],"randomized":[15],"CRCW":[16],"PRAM.":[17],"Specifically,":[18],"we":[19,146],"show":[20,59],"how":[21,60],"to":[22,61,140],"build":[23],"the":[24,32,63,86,91,111,129,136],"hull":[26,65,93],"n":[28,67],"presorted":[29],"points":[30,70],"in":[31,34,47,71,90,128],"plane":[33],"O(1)":[35],"time":[36,50,74],"using":[37,51,75],"O(n":[38,76],"log":[39,77],"n)":[40,49,73],"work,":[41,53,79],"with":[42,54,80],"n-exponential":[43,55,81,143],"probability,":[44,82],"or,":[45],"alternately,":[46],"O(log\u2217":[48],"O(n)":[52],"probability.":[56],"also":[58],"find":[62],"unsorted":[68,107],"planar":[69],"O(log":[72],"h)":[78],"where":[83],"h":[84],"is":[85,95],"edges":[89],"(h":[94],"O(n),":[96],"but":[97],"can":[98],"be":[99],"as":[100,102],"small":[101],"O(1)).":[103],"Our":[104],"algorithm":[105],"inputs":[108],"depends":[109],"use":[112,147],"new":[114,149],"in-place":[115],"procedures,":[116],"that":[117,120,132],"is,":[118],"procedures":[119],"are":[121],"defined":[122],"subset":[125],"elements":[127],"input":[130],"and":[131],"work":[133],"without":[134],"reordering":[135],"input.":[137],"In":[138],"order":[139],"achieve":[141],"our":[142],"confidence":[144],"bounds":[145],"technique":[151],"called":[152],"failure":[153],"sweeping.":[154]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}