Efficient sampling of random permutations

We show how to uniformly distribute data at random (not to be confounded with permutation routing) in two settings that are able to deal with massive data: coarse grained parallelism and external memory. In contrast to previously known work for parallel setups, our method is able to fulfill the three criteria of uniformity, work-optimality and balance among the processors simultaneously. To guarantee the uniformity we investigate the matrix of communication requests between the processors. We show that its distribution is a generalization of the multivariate hypergeometric distribution and we give algorithms to sample it efficiently in the two settings.