Designing fault-tolerant systems using automorphisms

Abstract

This paper presents a general theory for modeling and designing fault-tolerant multiprocessor systems in a systematic and efficient manner. We are concerned here with structural fault tolerance, defined as the ability to reconfigure around faults in order to preserve the interconnection structure of a multiprocessor. We represent multiprocessor systems by graphs whose node sets denote processors and whose edge sets denote dedicated interprocessor links. The fault-tolerant design and reconfiguration process of a multiprocessor is modeled by graph automorphisms. This automorphism-based methodology also models some important practical design features not previously addressed, including applicability to any multiprocessor structure and any number of faults. Low redundancy and efficient reconfigurability are also addressed. We apply our approach directly to a class of regular multiprocessor graphs termed circulant. For noncirculant graphs we give an algorithm to construct their circulant edge supergraphs efficiently. An application of the theory to the design of fault-tolerant hypercube multiprocessors is described. The resulting designs are shown to be far superior to those proposed in previous work.