Mapping of fault-tolerant permutations in omega interconnection network

Abstract

This paper presents a comprehensive treatment of the fault-tolerant characteristics of Omega interconnection network, which is a typical member of a class of non-redundant multistage interconnection networks characterised by the full-access property and unique-path property, in the presence of single faulty switching element in the network. A significant amount of research works has already been made in making a multistage interconnection network fault-tolerant by introducing redundancy in the network, which in its turn, increases the cost and complexity of the system. The extent to which an Omega network can be considered to be fault-tolerant in the presence of single faulty switching element and without the introduction of any redundancy, has been explored in this paper. Several claims, together with the corresponding proofs, have been made in this respect. In view of the unique-path property of this non-redundant network, every permutation is definitely not attainable in the presence of faults in the network; but, even a set of some fault-tolerant permutations, as discussed in this paper, may be of immense help in a distributed computing environment, which is characterised by the absence of any preference amongst all the possible permutations.