Randomized permutations in a coarse grained parallel environment

We show how to uniformly distribute data at random (not to be confounded with permutation routing) in a coarse grained parallel environment with p processors. In contrast to previously known work, our method is able to fulfill the three goals 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 compute it efficiently.