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Improved Mixing Time Bounds for the Thorp Shuffle

Published online by Cambridge University Press:  07 December 2012

BEN MORRIS
BEN MORRIS*
Affiliation:
Department of Mathematics, University of California, Davis, CA 95616, USA (e-mail: morris@math.ucdavis.edu)
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Abstract

E. Thorp introduced the following card shuffling model. Suppose the number of cards is even. Cut the deck into two equal piles, then interleave them as follows. Choose the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then choose from the other pile. Continue this way, flipping an independent coin for each pair, until both piles are empty.

We prove an upper bound of O(d3) for the mixing time of the Thorp shuffle with 2d cards, improving on the best known bound of O(d4). As a consequence, we obtain an improved bound on the time required to encrypt a binary message of length d using the Thorp shuffle.

Keywords

Primary 60J10

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 1 , January 2013 , pp. 118 - 132
Copyright
Copyright © Cambridge University Press 2012

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