Fault-tolerant sorting algorithm on hypercube multicomputers

Abstract

In this paper, algorithmic fault-tolerant techniques are introduced for sorting algorithms on n-dimensional hypercube multicomputers. We propose a fault-tolerant sorting algorithm that can tolerate up to n − 1 faulty processors. First, we indicate that the bitonic sorting algorithm can perform sorting operations correctly on hypercubes with one faulty processor. In order to tolerate up to r ⩽ n − 1 faulty processors, a partition algorithm is presented. The algorithm partitions the original hypercube with the minimum number of cuts into a set of subcubes such that each subcube has at most one faulty processor. The bitonic sorting algorithm can then be applied in each subcube correctly. Finally, each subcube is viewed as a node and a bitonic-like sorting procedure is applied to the subcubes with little communication overhead. In addition, we implement our algorithm on NCUBE/7 MIMD hypercube machines with 64 processors. The simulation results show that the performance of our fault-tolerant sorting algorithm on hypercubes is better than the approach for fording the maximal fault-free subcubes.