Ring embedding in multicomputer networks with faulty nodes

Abstract

The hypercube is one of the most versatile and efficient topologies yet discovered for parallel computation. It is well suited for the parallel execution of various algorithms for many application areas because of its regularity and their relatively small number of interprocessor connections. Recently, the mesh that is a rectangular grid-type array, and torus have been drawing a considerable attention as topologies for multiprocessor interconnection networks due to its simple, regular, and scalable architecture. As the number of nodes in a multicomputers increases, the probability that some node fails also increases. To increase the reliability of the multicomputers, efficient fault-tolerant schemes in multicomputers are necessary. There is an increasing interest in the problem of embedding graphs in faulty hypercubes. The embedding graphs such as rings[1, 2, 3, 5, 6], meshes[8], trees and so on, in faulty hypercubes, have been investigated by many researchers. Of these research results, we are particularly interested in the embedding of rings in faulty hypercubes. Many ring embedding algorithms for faulty hypercubes have been developed[1, 2, 3, 4, 5, 6]. Fault-tolerance in tori and meshes has been studied by several researchers, and several interesting techniques have been proposed, including fault-tolerant routing schemes[37, 38]. Ma et al. [32, 33] studied the problem of embedding d-dimensional meshes or tori in c-dimensional meshes or tori. Several topics related to the embedding in a faulty mesh have been studied previously including embedding linear arrays[34, 35], Hamiltonian cycles[31], and binary trees in a mesh with faulty nodes. Furthermore, it has been proved that embedding a Hamiltonian cycle in a mesh with arbitrary faulty nodes is NP-complete[30], and hence no efficient algorithm exists unless P=NP. Hedetniemi et al.[31] propose a ring embedding method in a mesh with a single faulty node. In this thesis, we consider tasks that require a ring stru...