Diagnosability of enhanced hypercubes

An enhanced hypercube is obtained by adding 2^n-1 more links to a regular hypercube of 2ⁿ processors. It has been shown that enhanced hypercubes have very good improvements over regular hypercubes in many measurements such as mean internode distance, diameter and traffic density. This paper proves that in the aspect of diagnosability, enhanced hypercubes also achieve improvements. Two diagnosis strategies, both using the well-known PMC diagnostic model, are studied: the precise (one-step) strategy proposed by Preparata, Metze and Chien (1967), and the pessimistic strategy proposed by Friedman (1975). Under the precise strategy, the diagnosability is shown to be increased to n+1 in enhanced hypercubes. (In regular hypercubes, the diagnosability is n under this strategy). Under the pessimistic strategy, the diagnosability is shown to be increased to 2n. (In regular hypercubes, the diagnosability under this strategy is 2n-2). Since the failure probability of one node is fairly low nowadays, so that the increase of diagnosability by one or two will considerably enhance the system´s self-diagnostic capability, and considering the fact that diagnosability does not “easily” increase as the links in networks do, these improvements are noticeable