A Simple Randomization Procedure
Abstract
SUMMARY: The paper describes a randomization procedure consisting in distributing a deck of cards into 10 decks using random decimal digits and repeating this step with each deck consisting of three or more cards. One random digit is used for randomizing a deck of two cards. This procedure, which is essentially a particular case of a general procedure described by Rao (1961), is called the multistage randomization procedure, or MRP. Some applications are described. A recursive formula is given for the expected number of random digits required by MRP for the randomization of n symbols. A measure of the efficiency of a randomization procedure is presented. The efficiency of MRP is compared with the efficiencies of two other randomization procedures, and it is proved that MRP has an asymptotic efficiency of 100 per cent.
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
The recursive divide-and-conquer parallel shuffling approaches RS and MergeShuffle have O(n log n) work complexity.
“The parallel work complexity of these recursive divide-and-conquer approaches is 𝑂 ( 𝑛 log ( 𝑛 )) .”
From Bandwidth-Optimal Random Shuffling for GPUs (2022) · cites this paper as [57]
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Bandwidth-Optimal Random Shuffling for GPUs
Mitchell, R., Stokes, D., Frank, E., & Holmes, G. (2022) · ACM Transactions on Parallel Computing · doi:10.1145/3505287 · Cited by 6 · see citing works
“A parallel divide-and-conquer shuffling algorithm is independently proposed by Rao [50] and Sandelius [54] (we refer to this algorithm as RS).”
Method
- Authors
- Sandelius, M.
- Affiliations
- Åmål, Sweden
- Corresponding author
- Sandelius, Martin
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1962-07-01
- Volume
- 24
- Issue
- 2
- Pages
- 472-481
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2904583894
- Cited by
- 13
- References
- 0
- Citations by year
- 2024: 1 · 2022: 2 · 2017: 1 · 2015: 2 · 2014: 1
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Survey Sampling and Estimation Techniques
- Keywords
- randomization procedures, card shuffling, asymptotic efficiency
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