Fast Permuting on Disk Arrays

Abstract

We present fast algorithms to accomplish common classes of permutations on parallel disk systems. Vitter and Shriver introduced a parallel I/O model and proved an asymptotically tight bound on the number of parallel I/Os needed to perform a general permutation. They demonstrated, however, that at least one type of permutation-matrix transpose-can be performed with fewer parallel I/Os than the lower bound for general permutations. This paper generalizes the Vitter-Shriver matrix-transpose result, showing that other classes of permutations can be performed with fewer parallel I/Os than the general permutation bound in many cases. We show how to perform bit-permute/complement (BPC) permutations, a class including matrix transpose and many other common permutations, with fewer parallel I/Os than general permutations. We also present a fast algorithm to perform bit-matrix-multiply/complement (BMMC) permutations. The algorithms for these permutations are built from restricted classes of permutations that we define, each requiring only one pass over the data. All the permutation algorithms presented in this paper are deterministic and are easily performed on-line.