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This article introduces an algorithm, MergeShuffle, which is an extremelyefficient algorithm to generate random permutations (or to randomly permute anexisting array). It is easy to implement, runs in $n\log_2 n + O(1)$ time, isin-place, uses $n\log_2 n + \Theta(n)$ random bits, and can be parallelizedaccross any number of processes, in a shared-memory PRAM model. Finally, ourpreliminary simulations using OpenMP suggest it is more efficient than theRao-Sandelius algorithm, one of the fastest existing random permutationalgorithms.  We also show how it is possible to further reduce the number of random bitsconsumed, by introducing a second algorithm BalancedShuffle, a variant of theRao-Sandelius algorithm which is more conservative in the way it recursivelypartitions arrays to be shuffled. While this algorithm is of lesser practicalinterest, we believe it may be of theoretical value.  Our full code is available at: https://github.com/axel-bacher/mergeshuffle

MergeShuffle: A Very Fast, Parallel Random Permutation Algorithm