Random Records and Cuttings in Split Trees: Extended Abstract
We study the number of records in random split trees on $n$ randomly labelled vertices. Equivalently the number of random cuttings required to eliminate an arbitrary random split tree can be studied. After normalization the distributions are shown to be asymptotically $1$-stable. This work is a gene...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3570/pdf |
| Summary: | We study the number of records in random split trees on $n$ randomly labelled vertices. Equivalently the number of random cuttings required to eliminate an arbitrary random split tree can be studied. After normalization the distributions are shown to be asymptotically $1$-stable. This work is a generalization of our earlier results for the random binary search tree which is one specific case of split trees. Other important examples of split trees include $m$-ary search trees, quadtrees, median of $(2k+1)$-trees, simplex trees, tries and digital search trees. |
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| ISSN: | 1365-8050 |