MapReduce Parallel Cuckoo Hashing and Oblivious RAM Simulations

We present an efficient algorithm for performing cuckoo hashing in the MapReduce parallel model of computation and we show how this result in turn leads to improved methods for performing data-oblivious RAM simulations. Our contributions involve a number of seemingly unrelated new results, including: a parallel MapReduce cuckoo hashing algorithm that runs in O(log n) time and uses O(n) total work, with very high probability a reduction of data-oblivious simulation of sparse-streaming MapReduce algorithms to oblivious sorting an external-memory data-oblivious sorting algorithm using O((N/B) log^2_(M/B) (N/B)) I/Os constant-memory data-oblivious RAM simulation with O(log^2 n) amortized time overhead, with very high probability, or with expected O(log2 n) amortized time overhead and better constant factors sublinear-memory data-oblivious RAM simulation with O(n^nu) private memory and O(log n) amortized time overhead, with very high probability, for constant nu > 0. This last result is, in fact, the main result of this paper, since it is asymptotically optimal and is for the more realistic setting with respect to private memory size.