An Efficient Parallel Sorting Algorithm on Metacube Multiprocessors

Abstract

Parallel sorting algorithms in hypercubes have been studied extensively. One of the practical parallel sorting algorithms is Bitonic Sort, which is implemented in O(n ²) time for sorting N = 2ⁿ numbers in an n-cube. A versatile family of interconnection networks alternative to hypercube, called metacube, was proposed for building extremely large scale multiprocessor systems with a small number of links per node. A metacube MC(k,m) connects $2^{2^km+k}$ nodes with only k + m links per node. In this paper, we present an efficient sorting algorithm on metacube multiprocessors. The proposed sorting algorithm is based on the Batcher’s bitonic sorting algorithm. In order to perform the parallel sorting efficiently in metacube, we give a new presentation of the metacube such that the communications required by the algorithm can be done efficiently with gather and scatter operations. The parallel bitonic sort algorithm implemented in metacubes with the new presentation runs in O(2^k m + k)² computation steps and O(2^k m(2k + 1) + k)² communication steps.