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An efficient method for generating a discrete uniform distribution using a biased random source

Part of: Theory of computing Algorithms - Computer Science

Published online by Cambridge University Press:  07 March 2023

Xiaoyu Lei
Xiaoyu Lei*
Affiliation:
The University of Chicago
*
*Postal address: 5747 South Ellis Avenue, Chicago, Illinois, USA. Email: leixy@uchicago.edu
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Abstract

We present an efficient algorithm to generate a discrete uniform distribution on a set of p elements using a biased random source for p prime. The algorithm generalizes Von Neumann’s method and improves the computational efficiency of Dijkstra’s method. In addition, the algorithm is extended to generate a discrete uniform distribution on any finite set based on the prime factorization of integers. The average running time of the proposed algorithm is overall sublinear: $\operatorname{O}\!(n/\log n)$.

Keywords

Random numbersprobability theory

MSC classification

Primary: 68W20: Randomized algorithms
Secondary: 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 3 , September 2023 , pp. 1069 - 1078
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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References

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