A repertoire for additive functionals of uniformly distributed m-ary search trees
Using recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on $m$-ary search trees on $n$ keys with toll sequence $(i) n^α$ with $α ≥ 0 (α =0$ and $α =1$ correspond roughly to the space requirement and tot...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3370/pdf |
| _version_ | 1797270636312133632 |
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| author | james Allen fill Nevin Kapur |
| author_facet | james Allen fill Nevin Kapur |
| author_sort | james Allen fill |
| collection | DOAJ |
| description | Using recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on $m$-ary search trees on $n$ keys with toll sequence $(i) n^α$ with $α ≥ 0 (α =0$ and $α =1$ correspond roughly to the space requirement and total path length, respectively); $(ii) ln \binom{n} {m-1}$, which corresponds to the so-called shape functional; and $(iii) $$1$$_{n=m-1}$, which corresponds to the number of leaves. |
| first_indexed | 2024-04-25T02:07:25Z |
| format | Article |
| id | doaj.art-85110cfaf9604dd19f2bb1ea8356a62b |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:07:25Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-85110cfaf9604dd19f2bb1ea8356a62b2024-03-07T14:30:52ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AD,...Proceedings10.46298/dmtcs.33703370A repertoire for additive functionals of uniformly distributed m-ary search treesjames Allen fillNevin Kapur0Department of Computer ScienceUsing recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on $m$-ary search trees on $n$ keys with toll sequence $(i) n^α$ with $α ≥ 0 (α =0$ and $α =1$ correspond roughly to the space requirement and total path length, respectively); $(ii) ln \binom{n} {m-1}$, which corresponds to the so-called shape functional; and $(iii) $$1$$_{n=m-1}$, which corresponds to the number of leaves.https://dmtcs.episciences.org/3370/pdfmethod of momentslimit lawshadamard productsadditive functionalssearch treesleavesspace requirementsingularity analysisshape functional[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-cg] computer science [cs]/computational geometry [cs.cg][info.info-hc] computer science [cs]/human-computer interaction [cs.hc] |
| spellingShingle | james Allen fill Nevin Kapur A repertoire for additive functionals of uniformly distributed m-ary search trees Discrete Mathematics & Theoretical Computer Science method of moments limit laws hadamard products additive functionals search trees leaves space requirement singularity analysis shape functional [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] [info.info-hc] computer science [cs]/human-computer interaction [cs.hc] |
| title | A repertoire for additive functionals of uniformly distributed m-ary search trees |
| title_full | A repertoire for additive functionals of uniformly distributed m-ary search trees |
| title_fullStr | A repertoire for additive functionals of uniformly distributed m-ary search trees |
| title_full_unstemmed | A repertoire for additive functionals of uniformly distributed m-ary search trees |
| title_short | A repertoire for additive functionals of uniformly distributed m-ary search trees |
| title_sort | repertoire for additive functionals of uniformly distributed m ary search trees |
| topic | method of moments limit laws hadamard products additive functionals search trees leaves space requirement singularity analysis shape functional [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] [info.info-hc] computer science [cs]/human-computer interaction [cs.hc] |
| url | https://dmtcs.episciences.org/3370/pdf |
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