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A simple randomized algorithm for generating a uniformly distributed random permutation of size n is investigated. It works in time O ( n P + T comm ( n P , P) + T prefix (P)) on P processors with high probability, where T comm ( k , P ) is the time for randomly sending or receiving k elements on each processor and T prefix ( P ) is the time for computing a prefix sum. The algorithm can be directly translated into an optimal external memory algorithm if fast memory for √ nB (1 + o (1)) + O ( B ) elements is available where B is the page size. Due to its simplicity, the same algorithm even outperforms the straightforward method on mainstream workstations if the cache is taken to be the fast memory and the main memory is treated like external memory. The algorithm is almost four times faster on a MIPS R10000 machine.

The theory of powerlists was recently introduced by Jayadev Misra (1994). Powerlists can be used to specify and verify certain parallel algorithms, using a notation similar to functional programming languages. In contrast to sequential languages the powerlist notation has constructs for expressing balanced divisions of lists. We study how Prefix Sum , a fundamental parallel algorithm, can be tailored for efficient execution on hypercubic architectures. Then we derive a strategy for mapping most powerlist functions to efficient programs for hypercubic architectures.

We present an O(logn) prefix sum algorithm for n data distributed across n processors, and an O(logn) matrix multiplication algorithm of n x n arrays using n3 processors interconnected by a 3-dimensional mesh, using wormhole routing communication.