Conditional diagnosability of hypermesh optical multiprocessor systems under the PMC model

The hypermeshes are a family of promising optical interconnection topologies for multiprocessor systems. In this paper, the conditional diagnosability of the hypermesh optical multiprocessor systems, under the PMC model, is determined. We derive that the conditional diagnosability of k(n)-hypermesh is 4n (k - 1) - 4k + 1, where n >= 3 and k >= 5. This result shows that the hypermesh optical multiprocessor systems possess strong self-diagnosing abilities.