{"title":"一致多维二叉树中节点的联合分布","authors":"R. Kemp","doi":"10.1002/(SICI)1098-2418(199810/12)13:3/4%3C261::AID-RSA5%3E3.0.CO;2-T","DOIUrl":null,"url":null,"abstract":"Multidimensional binary trees represent a symbiosis of trees and tries, and they essentially arise in the construction of search trees for multidimensional keys. The set of nodes in a d-dimensional binary tree can be partitioned into layers according to the nodes appearing in the ith dimension. We determine the exact distribution of the number of nodes with zero, one, and two sons in a specified layer and show that jointly the three types of nodes asymptotically have a trivariate normal distribution in each layer. That trivariate normal distribution is completely characterized. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 261–283, 1998","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On the joint distribution of the nodes in uniform multidimensional binary trees\",\"authors\":\"R. Kemp\",\"doi\":\"10.1002/(SICI)1098-2418(199810/12)13:3/4%3C261::AID-RSA5%3E3.0.CO;2-T\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Multidimensional binary trees represent a symbiosis of trees and tries, and they essentially arise in the construction of search trees for multidimensional keys. The set of nodes in a d-dimensional binary tree can be partitioned into layers according to the nodes appearing in the ith dimension. We determine the exact distribution of the number of nodes with zero, one, and two sons in a specified layer and show that jointly the three types of nodes asymptotically have a trivariate normal distribution in each layer. That trivariate normal distribution is completely characterized. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 261–283, 1998\",\"PeriodicalId\":303496,\"journal\":{\"name\":\"Random Struct. Algorithms\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Struct. Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/(SICI)1098-2418(199810/12)13:3/4%3C261::AID-RSA5%3E3.0.CO;2-T\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(199810/12)13:3/4%3C261::AID-RSA5%3E3.0.CO;2-T","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
On the joint distribution of the nodes in uniform multidimensional binary trees
Multidimensional binary trees represent a symbiosis of trees and tries, and they essentially arise in the construction of search trees for multidimensional keys. The set of nodes in a d-dimensional binary tree can be partitioned into layers according to the nodes appearing in the ith dimension. We determine the exact distribution of the number of nodes with zero, one, and two sons in a specified layer and show that jointly the three types of nodes asymptotically have a trivariate normal distribution in each layer. That trivariate normal distribution is completely characterized. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 261–283, 1998
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