An Efficient Method To Generate A Discrete Uniform Distribution Using A Biased Random Source

TL;DR

This paper introduces an efficient algorithm for generating discrete uniform distributions from biased sources, extending classical methods and achieving sublinear time complexity for prime-sized sets.

Contribution

It generalizes Von Neumann's method, improves Dijkstra's approach, and extends to arbitrary finite sets based on prime factorization, enhancing efficiency and applicability.

Findings

Achieves sublinear time complexity of O(n/log n)

Generalizes classical methods for biased sources

Extends to arbitrary finite sets using prime factorization

Abstract

This article presents 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 computational efficiency of Dijkstra's method. In addition, the algorithm is extended to generate discrete uniform distribution on any finite set based on the prime factorization of integers. The time complexity of the proposed algorithm is overall sublinear $\operatorname{O}(n/\log n)$