Fault-tolerant ring embedding in de Bruijn networks

A method of embedding a ring in a d-ary de Bruijn multiprocessor network in the event of multiple node (processor) failures is presented. In particular, the algorithm guarantees that a (2ⁿ-n-1)-node ring will be found in a binary de Bruijn network with a single faulty node, where 2ⁿ is the total number of nodes in the network. It is also shown that a (dⁿ-1)-node ring can always be found in the presence of d-1 link failures, when d is a prime power and the network contains dⁿ nodes. The latter is accomplished by constructing d-1 edge-disjoint cycles each of length dⁿ-1. A modification of the graph that allows it to admit a Hamiltonian cycle in the event of d-1 edge failures is also discussed