Conditional Fault Tolerance of Hypermesh Optical Interconnection Networks

Fault tolerance is especially important for interconnection networks, vastly influencing the performance of the parallel processing systems underlying the corresponding networks. This paper studies the fault tolerance of radix-k n-dimensional hypermesh optical interconnection networks, determines the connectivity of partial hypermesh, and derives the conditional connectivity of hypermesh provided that each adjacent set cannot be faulty simultaneously. Under this condition, the hypermesh networks can tolerate up to 2n(k-1)-k-1 fault processors without being disrupted, implying that when the number of dimension n (respectively, radix-k) is a fixed value in the hypermesh network, the larger the value of radix-k (respectively, dimension n) is, the higher the reliability and availability of the network becomes.