{"id":"https://openalex.org/W1992422944","doi":"https://doi.org/10.1017/s0963548302005138","title":"Quickselect and the Dickman Function","display_name":"Quickselect and the Dickman Function","publication_year":2002,"publication_date":"2002-07-01","ids":{"openalex":"https://openalex.org/W1992422944","doi":"https://doi.org/10.1017/s0963548302005138","mag":"1992422944"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548302005138","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005138","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and 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/A5003984705","display_name":"Hsien\u2010Kuei Hwang","orcid":"https://orcid.org/0000-0002-9410-6476"},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]},{"id":"https://openalex.org/I4210141710","display_name":"Institute of Statistical Science, Academia Sinica","ror":"https://ror.org/044gv5910","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210141710","https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"HSIEN-KUEI HWANG","raw_affiliation_strings":["Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail:","Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail: hkhwang@stat.sinica.edu.tw)#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail:","institution_ids":["https://openalex.org/I4210141710"]},{"raw_affiliation_string":"Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail: hkhwang@stat.sinica.edu.tw)#TAB#","institution_ids":["https://openalex.org/I84653119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015787840","display_name":"Tsung\u2010Hsi Tsai","orcid":null},"institutions":[{"id":"https://openalex.org/I4210141710","display_name":"Institute of Statistical Science, Academia Sinica","ror":"https://ror.org/044gv5910","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210141710","https://openalex.org/I84653119"]},{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"TSUNG-HSI TSAI","raw_affiliation_strings":["Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail:","Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail: hkhwang@stat.sinica.edu.tw)#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail:","institution_ids":["https://openalex.org/I4210141710"]},{"raw_affiliation_string":"Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail: hkhwang@stat.sinica.edu.tw)#TAB#","institution_ids":["https://openalex.org/I84653119"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003984705"],"corresponding_institution_ids":["https://openalex.org/I4210141710","https://openalex.org/I84653119"],"apc_list":null,"apc_paid":null,"fwci":6.1429,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.96713442,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"353","last_page":"371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9972000122070312,"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/limiting","display_name":"Limiting","score":0.8359146118164062},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7692362070083618},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6685965061187744},{"id":"https://openalex.org/keywords/random-permutation","display_name":"Random permutation","score":0.5670515894889832},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5590751767158508},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.55324387550354},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49524131417274475},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.42775946855545044},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.4184815287590027},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38434308767318726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12161961197853088},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11437296867370605},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09022876620292664}],"concepts":[{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.8359146118164062},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7692362070083618},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6685965061187744},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.5670515894889832},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5590751767158508},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.55324387550354},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49524131417274475},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.42775946855545044},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.4184815287590027},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38434308767318726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12161961197853088},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11437296867370605},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09022876620292664},{"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/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548302005138","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005138","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4399999976158142,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W192578068","https://openalex.org/W1492697544","https://openalex.org/W1497373391","https://openalex.org/W1546072503","https://openalex.org/W1562455717","https://openalex.org/W1792966054","https://openalex.org/W1965155608","https://openalex.org/W1990017905","https://openalex.org/W1996847651","https://openalex.org/W1997773225","https://openalex.org/W2002330177","https://openalex.org/W2007046591","https://openalex.org/W2013150049","https://openalex.org/W2013390824","https://openalex.org/W2017427035","https://openalex.org/W2023132896","https://openalex.org/W2037312735","https://openalex.org/W2084833267","https://openalex.org/W2088772065","https://openalex.org/W2102753310","https://openalex.org/W2114754143","https://openalex.org/W2140092022","https://openalex.org/W2147377632","https://openalex.org/W2151368268","https://openalex.org/W2316865302","https://openalex.org/W2330907628","https://openalex.org/W2498839538","https://openalex.org/W2608452798","https://openalex.org/W2798461040","https://openalex.org/W3009825533"],"related_works":["https://openalex.org/W2393575620","https://openalex.org/W2023083137","https://openalex.org/W2775312429","https://openalex.org/W3044811636","https://openalex.org/W2066602736","https://openalex.org/W2341755444","https://openalex.org/W1992422944","https://openalex.org/W38971153","https://openalex.org/W1987763401","https://openalex.org/W3094758868"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,7,26,38,45],"limiting":[4,42],"distribution":[5,43],"of":[6,9,21,44,47],"number":[8,46],"comparisons":[10],"used":[11],"by":[12],"Hoare's":[13],"quickselect":[14],"algorithm":[15],"when":[16],"given":[17],"a":[18],"random":[19],"permutation":[20],"n":[22,35],"elements":[23],"for":[24],"finding":[25],"m":[27,31],"th-smallest":[28],"element,":[29],"where":[30],"=":[32],"o":[33],"(":[34],"),":[36],"is":[37,49],"Dickman":[39],"function.":[40],"The":[41],"exchanges":[48],"also":[50],"derived.":[51]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
