Cubesort: An optimal sorting algorithm for feasible parallel computers

Abstract

This paper studies the problem of sorting N items on a P processor parallel machine, where N≥P. The central result of the paper is a new algorithm, called cubesort, that sorts N=P^1+1/k items in O(k P^1/k log P) time using a P processor shuffle-exchange. Thus for any positive constant k, cubesort provides an asymptotically optimal speed-up over sequential sorting. Cubesort also sorts N = P log P items using a P processor shuffle-exchange in O(log³ P/loglog P) time. Both of these results are faster than any previously published algorithms for the given problems. Cubesort also provides asymptotically optimal sorting algorithms for a wide range of parallel computers, including the cube-connected cycles and the hypercube. An important extension of the central result is an algorithm that simulates a single step of a Priority-CRCW PRAM with N processors and N words of memory on a P processor shuffle-exchange machine in O(k P^1/k log P) time, where N=P^1+1/k.