{"id":"https://openalex.org/W2168559467","doi":"https://doi.org/10.1016/0022-0000(82)90004-6","title":"The average height of binary trees and other simple trees","display_name":"The average height of binary trees and other simple trees","publication_year":1982,"publication_date":"1982-10-01","ids":{"openalex":"https://openalex.org/W2168559467","doi":"https://doi.org/10.1016/0022-0000(82)90004-6","mag":"2168559467"},"language":"en","primary_location":{"id":"doi:10.1016/0022-0000(82)90004-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0022-0000(82)90004-6","pdf_url":null,"source":{"id":"https://openalex.org/S141020589","display_name":"Journal of Computer and System Sciences","issn_l":"0022-0000","issn":["0022-0000","1090-2724"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computer and System Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00076505","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018743761","display_name":"Philippe Flajolet","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Philippe Flajolet","raw_affiliation_strings":["INRIA, 78150 Rocquencourt, France"],"affiliations":[{"raw_affiliation_string":"INRIA, 78150 Rocquencourt, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035952740","display_name":"Andrew Odlyzko","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Odlyzko","raw_affiliation_strings":["Bell Laboratories, Murray Hill, New Jersey 07974, USA"],"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Murray Hill, New Jersey 07974, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018743761"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":{"value":2520,"currency":"USD","value_usd":2520},"apc_paid":null,"fwci":13.8184,"has_fulltext":false,"cited_by_count":254,"citation_normalized_percentile":{"value":0.99724518,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"25","issue":"2","first_page":"171","last_page":"213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9879999756813049,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9879999756813049,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11106","display_name":"Data Management and Algorithms","score":0.972599983215332,"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/tree-traversal","display_name":"Tree traversal","score":0.8576704263687134},{"id":"https://openalex.org/keywords/weight-balanced-tree","display_name":"Weight-balanced tree","score":0.7851517200469971},{"id":"https://openalex.org/keywords/random-binary-tree","display_name":"Random binary tree","score":0.7721110582351685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7603765726089478},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.7473165988922119},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.6663210391998291},{"id":"https://openalex.org/keywords/de-bruijn-sequence","display_name":"De Bruijn sequence","score":0.6548821926116943},{"id":"https://openalex.org/keywords/optimal-binary-search-tree","display_name":"Optimal binary search tree","score":0.5776633620262146},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5729258060455322},{"id":"https://openalex.org/keywords/binary-expression-tree","display_name":"Binary expression tree","score":0.5537531971931458},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5483251214027405},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5412766933441162},{"id":"https://openalex.org/keywords/ternary-search-tree","display_name":"Ternary search tree","score":0.5381627082824707},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.5135136246681213},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4916754364967346},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.401601642370224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38323548436164856},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.2031065821647644},{"id":"https://openalex.org/keywords/interval-tree","display_name":"Interval tree","score":0.17012807726860046},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.13194140791893005},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11266690492630005}],"concepts":[{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.8576704263687134},{"id":"https://openalex.org/C57900377","wikidata":"https://www.wikidata.org/wiki/Q7979855","display_name":"Weight-balanced tree","level":4,"score":0.7851517200469971},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.7721110582351685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7603765726089478},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.7473165988922119},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.6663210391998291},{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.6548821926116943},{"id":"https://openalex.org/C27628562","wikidata":"https://www.wikidata.org/wiki/Q17154715","display_name":"Optimal binary search tree","level":5,"score":0.5776633620262146},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5729258060455322},{"id":"https://openalex.org/C166055160","wikidata":"https://www.wikidata.org/wiki/Q4913895","display_name":"Binary expression tree","level":3,"score":0.5537531971931458},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5483251214027405},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5412766933441162},{"id":"https://openalex.org/C136519935","wikidata":"https://www.wikidata.org/wiki/Q2859802","display_name":"Ternary search tree","level":5,"score":0.5381627082824707},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.5135136246681213},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4916754364967346},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.401601642370224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38323548436164856},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.2031065821647644},{"id":"https://openalex.org/C84927040","wikidata":"https://www.wikidata.org/wiki/Q6057306","display_name":"Interval tree","level":4,"score":0.17012807726860046},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.13194140791893005},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11266690492630005},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0022-0000(82)90004-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0022-0000(82)90004-6","pdf_url":null,"source":{"id":"https://openalex.org/S141020589","display_name":"Journal of Computer and System Sciences","issn_l":"0022-0000","issn":["0022-0000","1090-2724"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computer and System Sciences","raw_type":"journal-article"},{"id":"pmh:oai:HAL:inria-00076505v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00076505","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-0056, INRIA. 1981","raw_type":"Reports"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00076505v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00076505","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-0056, INRIA. 1981","raw_type":"Reports"},"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W194256761","https://openalex.org/W594514321","https://openalex.org/W1537139364","https://openalex.org/W1562572594","https://openalex.org/W1965516463","https://openalex.org/W1981714789","https://openalex.org/W1983188796","https://openalex.org/W1993449345","https://openalex.org/W1998448131","https://openalex.org/W1999818096","https://openalex.org/W2045390532","https://openalex.org/W2049817705","https://openalex.org/W2066828720","https://openalex.org/W2070756504","https://openalex.org/W2089864510","https://openalex.org/W2098828803","https://openalex.org/W2159376684","https://openalex.org/W2167266655","https://openalex.org/W3198160809","https://openalex.org/W4239614637","https://openalex.org/W6607938699","https://openalex.org/W6632045946","https://openalex.org/W6672687485"],"related_works":["https://openalex.org/W2077383771","https://openalex.org/W3169685561","https://openalex.org/W2072924299","https://openalex.org/W2501849745","https://openalex.org/W1510719821","https://openalex.org/W1973074590","https://openalex.org/W1979520615","https://openalex.org/W2003946312","https://openalex.org/W3022865202","https://openalex.org/W2135212710"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}