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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.20700 |
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| _version_ | 1866909443998875648 |
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| author | Huber, Mark Vargas, Danny |
| author_facet | Huber, Mark Vargas, Danny |
| contents | In 1976, Knuth and Yao presented an algorithm for sampling from a finite distribution using flips of a fair coin that on average used the optimal number of flips. Here we show how to easily run their algorithm for the special case of rolling a fair die that uses memory linear in the input. Analysis of this algorithm yields a bound on the average number of coin flips needed that is slightly better than the original Knuth-Yao bound. This can then be extended to discrete distributions in a near optimal number of flips again using memory linear in the input. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal rolling of fair dice using fair coins Huber, Mark Vargas, Danny Data Structures and Algorithms Probability Computation 60-08, 68Q87 G.3; F.2.1 In 1976, Knuth and Yao presented an algorithm for sampling from a finite distribution using flips of a fair coin that on average used the optimal number of flips. Here we show how to easily run their algorithm for the special case of rolling a fair die that uses memory linear in the input. Analysis of this algorithm yields a bound on the average number of coin flips needed that is slightly better than the original Knuth-Yao bound. This can then be extended to discrete distributions in a near optimal number of flips again using memory linear in the input. |
| title | Optimal rolling of fair dice using fair coins |
| topic | Data Structures and Algorithms Probability Computation 60-08, 68Q87 G.3; F.2.1 |
| url | https://arxiv.org/abs/2412.20700 |