A Generalized Fault-Tolerant Sorting Algorithm on Product Network

Abstract

Product networks define a class of topologies that are used very often such as mesh, tori, and hypercube, etc. This paper proposes a generalized algorithm for fault-tolerant parallel sorting in the product networks. To tolerate multiple faulty nodes, product network is partitioned into a number of subgraphs such that each subgraph contains at most one fault. Our generalized sort algorithm is divided into two steps. First, a single-fault sorting operation is presented to correctly execute on each faulty subgraph is considered as a supernode, and a fault-tolerant multiway merge operation is presented to recursively merge two sorted subsequences into one sorted sequence. Our generalized sort algorithm can be applied on any product network if the factor graph of product graph can at least embed a ring structure. Further, we also show the time complexity of our sorting operations on the grid, hypercube, and petersen cube. The performance analysis illustrates that our generalized fault-tolerant sort algorithm is near-optimal.