Swapped (OTIS) Networks Built of Connected Basis Networks Are Maximally Fault Tolerant

An optical transpose interconnection system (OTIS) network with n
²
nodes is a two-level swapped architecture built of n copies of an n-node basis network that constitute its clusters. A simple rule for intercluster connectivity (node j in cluster i connected to node i in cluster j) leads to regularity, modularity, packageability, fault tolerance, and algorithmic efficiency of the resulting networks. We prove that an OTIS (swapped) network with a connected basis network possesses maximal fault tolerance, regardless of whether its basis network is maximally fault tolerant. We also show how the corresponding maximal number of node-disjoint paths between two nodes of a swapped network can be algorithmically constructed in a manner that is independent of the existence and construction of node-disjoint paths within its basis network. Our results are stronger than previously published results and they replace a number of proofs and constructions in the literature for specific basis networks. Additionally, we use our parallel path constructions to establish that the fault diameter and wide diameter of an OTIS network is no more than 4 units greater than its diameter.