Analysis of some statistics for increasing tree families
This paper deals with statistics concerning distances between randomly chosen nodes in varieties of increasing trees. Increasing trees are labelled rooted trees where labels along any branch from the root go in increasing order. Many mportant tree families that have applications in computer science...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2004-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/326/pdf |
| _version_ | 1797270202150289408 |
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| author | Alois Panholzer Helmut Prodinger |
| author_facet | Alois Panholzer Helmut Prodinger |
| author_sort | Alois Panholzer |
| collection | DOAJ |
| description | This paper deals with statistics concerning distances between randomly chosen nodes in varieties of increasing trees. Increasing trees are labelled rooted trees where labels along any branch from the root go in increasing order. Many mportant tree families that have applications in computer science or are used as probabilistic models in various applications, like \emphrecursive trees, heap-ordered trees or \emphbinary increasing trees (isomorphic to binary search trees) are members of this variety of trees. We consider the parameters \textitdepth of a randomly chosen node, \textitdistance between two randomly chosen nodes, and the generalisations where \textitp nodes are randomly chosen Under the restriction that the node-degrees are bounded, we can prove that all these parameters converge in law to the Normal distribution. This extends results obtained earlier for binary search trees and heap-ordered trees to a much larger class of structures. |
| first_indexed | 2024-04-25T02:00:31Z |
| format | Article |
| id | doaj.art-5a351a6ea7574616abe4b29db81ce485 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:31Z |
| publishDate | 2004-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-5a351a6ea7574616abe4b29db81ce4852024-03-07T15:06:37ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502004-01-01Vol. 6 no. 210.46298/dmtcs.326326Analysis of some statistics for increasing tree familiesAlois Panholzer0Helmut Prodinger1Institut für Diskrete Mathematik und Geometrie [Wien]The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]This paper deals with statistics concerning distances between randomly chosen nodes in varieties of increasing trees. Increasing trees are labelled rooted trees where labels along any branch from the root go in increasing order. Many mportant tree families that have applications in computer science or are used as probabilistic models in various applications, like \emphrecursive trees, heap-ordered trees or \emphbinary increasing trees (isomorphic to binary search trees) are members of this variety of trees. We consider the parameters \textitdepth of a randomly chosen node, \textitdistance between two randomly chosen nodes, and the generalisations where \textitp nodes are randomly chosen Under the restriction that the node-degrees are bounded, we can prove that all these parameters converge in law to the Normal distribution. This extends results obtained earlier for binary search trees and heap-ordered trees to a much larger class of structures.https://dmtcs.episciences.org/326/pdfincreasing treessteiner-distanceancestor-tree size[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Alois Panholzer Helmut Prodinger Analysis of some statistics for increasing tree families Discrete Mathematics & Theoretical Computer Science increasing trees steiner-distance ancestor-tree size [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Analysis of some statistics for increasing tree families |
| title_full | Analysis of some statistics for increasing tree families |
| title_fullStr | Analysis of some statistics for increasing tree families |
| title_full_unstemmed | Analysis of some statistics for increasing tree families |
| title_short | Analysis of some statistics for increasing tree families |
| title_sort | analysis of some statistics for increasing tree families |
| topic | increasing trees steiner-distance ancestor-tree size [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/326/pdf |
| work_keys_str_mv | AT aloispanholzer analysisofsomestatisticsforincreasingtreefamilies AT helmutprodinger analysisofsomestatisticsforincreasingtreefamilies |