{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T13:58:12Z","timestamp":1726149492024},"reference-count":21,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T00:00:00Z","timestamp":1659398400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2023,5]]},"abstract":"Abstract<\/jats:title>Given a permutation , its corresponding binary search tree is obtained by recursively inserting the values into a binary tree so that the label of each node is larger than the labels of its left subtree and smaller than the labels of its right subtree. In this article, we study the height of binary search trees drawn from the record\u2010biased model of permutations whose probability measure on the set of permutations is proportional to , where . We show that the height of a binary search tree built from a record\u2010biased permutation of size with parameter is of order , hence extending previous results of Devroye on the height or random binary search trees.<\/jats:p>","DOI":"10.1002\/rsa.21110","type":"journal-article","created":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T19:48:38Z","timestamp":1659469718000},"page":"623-644","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The height of record\u2010biased trees"],"prefix":"10.1002","volume":"62","author":[{"given":"Beno\u00eet","family":"Corsini","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, McGill University Montreal Quebec Canada"}]}],"member":"311","published-online":{"date-parts":[[2022,8,2]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1214\/20-AOP1503"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOP428"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOP750"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.4171\/000"},{"key":"e_1_2_6_6_1","unstructured":"N.Auger M.Bouvel C.Nicaud andC.Pivoteau Analysis of algorithms for permutations biased by their number of records arXiv preprint arXiv:1605.02905 2016."},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800042348"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20202"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01193752"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/5925.5930"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/765568.765572"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00026-009-0009-x"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v17-1698"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0040-5809(72)90035-4"},{"key":"e_1_2_6_15_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1968-0223256-9"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996611"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOP419"},{"key":"e_1_2_6_18_1","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996266"},{"key":"e_1_2_6_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/44.1-2.114"},{"key":"e_1_2_6_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/18-AOP1286"},{"key":"e_1_2_6_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90141-0"},{"key":"e_1_2_6_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/765568.765571"}],"container-title":["Random Structures & Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.21110","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/rsa.21110","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.21110","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T02:09:57Z","timestamp":1692583797000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.21110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,2]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["10.1002\/rsa.21110"],"URL":"https:\/\/doi.org\/10.1002\/rsa.21110","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,2]]},"assertion":[{"value":"2022-01-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-04-15","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-08-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}