Generating Random Permutations by Coin Tossing

Abstract

Several simple, classical, little-known algorithms in the statistics and computer science literature for generating random permutations by coin tossing are examined, analyzed, and implemented. These algorithms are either asymptotically optimal or close to being so in terms of the expected number of times the random bits are generated. In addition to asymptotic approximations to the expected complexity, we also clarify the corresponding variances, as well as the asymptotic distributions. A brief comparative discussion with numerical computations in a multicore system is also given.