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Exact Sublinear Binomial Sampling

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Abstract

Drawing a random variate from a given binomial distribution B(n, p) is an important subroutine in many large-scale simulations. The naive algorithm takes \(\mathcal {O}(n)\) time w.h.p. in the WordRAM model, which is too slow in many settings, though to its credit, it does not suffer from precision loss. The problem of sampling from a binomial distribution in sublinear time has been extensively studied and implemented in such packages as R [22] and the GNU Scientific Library  [11], however, all previous sublinear-time algorithms involve precision loss, which introduces artifacts such as discontinuities into the sampling. In this paper, we present the first algorithm, to the best of our knowledge, that samples binomial distributions in sublinear time with no precision loss. We assume that each bit of p can be obtained in \(\mathcal {O}(1)\) time.

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Notes

  1. The exponent of the polylog is not specified in their paper, and depends on such factors as the runtime to compute the digits of \(\sqrt{2\pi }\), but we note here that it is more than 1.

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Acknowledgments

We sincerely thank the reviewers for their helpful commments.

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Authors and Affiliations

  1. Rutgers University, New Brunswick, NJ, 08901, USA

    Martín Farach-Colton & Meng-Tsung Tsai

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  1. Martín Farach-Colton
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  2. Meng-Tsung Tsai
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Correspondence to Meng-Tsung Tsai.

Additional information

This research was supported by NSF Grants IIS-1247750 and CCF-1114930.

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Farach-Colton, M., Tsai, MT. Exact Sublinear Binomial Sampling. Algorithmica 73, 637–651 (2015). https://doi.org/10.1007/s00453-015-0077-8

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  • DOI: https://doi.org/10.1007/s00453-015-0077-8

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