A New Measure in System-Level Diagnosis of Hypercubes

Abstract

In this paper a new measure in system-level diagnosis for hypercube multicomputer systems is defined. One-step diagnosis of hypercubes which involves only one testing phase during which processors test each other is discussed. Two different kinds of one-step diagnosis are considered: one called one-step diagnosis and studied earlier by other researchers and the other called one-step diagnosis with the forbidden faulty sets (one-step-FFS) and studied first here in the context of application to hypercubes. One of the two main results presented here is a proof that the degree of diagnosability of the n-dimensional hypercube (for short, n-cube), where n ≥ 4 increases from n to 2n − 2 as the diagnosis strategy changes from the one-step strategy to the one-step-FFS strategy. The other main result is the proof that if the fault bound; i.e., the upper bound on the possible number of faulty processors, is kept to the same number n in both cases of one-step and one-step-FFS diagnosis, then the one-step-FFS strategy requires [n/2] + 1 testing links per processor, whereas the one-step strategy requires n testing links per processor. An algorithm for selecting ([n/2] + 1)n/2 (2-way) links in an n-cube for use as testing links is presented.