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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.11982 |
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| _version_ | 1866916102155534336 |
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| author | Lescanne, Pierre |
| author_facet | Lescanne, Pierre |
| contents | Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. R{é}my showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees. I extend this paradigm to Motzkin trees and Schr{ö}der trees and show that despite slight differences my algorithm that generates random Schr{ö}der trees has linear expected complexity and my algorithm that generates Motzkin trees is in O(n) expected complexity, only if we can implement a specific oracle with a O(1) complexity. For Motzkin trees, I propose a solution which works well for realistic values (up to size ten millions) and yields an efficient algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11982 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Holonomic equations and efficient random generation of binary trees Lescanne, Pierre Data Structures and Algorithms Computational Complexity Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. R{é}my showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees. I extend this paradigm to Motzkin trees and Schr{ö}der trees and show that despite slight differences my algorithm that generates random Schr{ö}der trees has linear expected complexity and my algorithm that generates Motzkin trees is in O(n) expected complexity, only if we can implement a specific oracle with a O(1) complexity. For Motzkin trees, I propose a solution which works well for realistic values (up to size ten millions) and yields an efficient algorithm. |
| title | Holonomic equations and efficient random generation of binary trees |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2205.11982 |