Number of mutual connections in neighborhoods and its application to self-diagnosable systems

摘要

This paper gives a set of discriminators (sufficient conditions) to identify the possibility of embedding optimal, highly structured systems on regular graphs for the purpose of self-diagnosis. The discrimination process is only a set of straightforward matrix computations; however, the discriminator is powerful and leads to the result that most of the typical graphs representing interconnection networks such as Cayley graphs can be embedded by the highly structured systems. The highly structured system has an O(|E|) fault-identification algorithm that can diagnose each of the units independently, locally and in any order, where |E| means the cardinality of the set of edges.