Conditional diagnosability of hypermeshes under the comparison model

The hypermeshes are a family of promising optical interconnection topologies for multiprocessor systems. This paper is concerned with the conditional diagnosability of hypermeshes under the comparison model. We prove that, for n⩾3n⩾3, k⩾4k⩾4, the conditional diagnosability of knkn-hypermesh is 3n(k−1)−2k−13n(k−1)−2k−1. This result shows that the hypermeshes possess strong self-diagnosing ability.

Research highlights
► The hypermeshes are a family of promising optical interconnection topologies for multiprocessor systems.
► We examine the connectivity of hypermeshes with some faulty nodes.
► We drive the conditional diagnosability of hypermeshes under the comparison model.
► The conditional diagnosability of k-ary n  -dimensional hypermeshes is 3n(k−1)−2k−13n(k−1)−2k−1 where n⩾3n⩾3, k⩾4k⩾4.