Fault-Tolerance Properties of deBruijn and Shuffle-Exchange Networks

W e study node fault-tolerance propert ies of the dary deBruij’n and shufle-exchange networks by appealing t o the algebraic structure of their underlying digraphs. In particular, we prove that both of these families of digraphs have connectivity equal t o their minimum degree. T h i s result is new in the case of the shuffle-exchange digraphs and can be extended f o r both famil ies t o characterize the pairs of vertices which haue d disjoint paths between them. Also, the analys is presented in our results paves the w a y t o a novel deterministic point-to-point routing algorithm which is capable of avoiding a large number of complete shuffle cycles in order-n, d-ary deBruijn and shuffle-exchange digraphs.