Fault-Tolerant Fixed Routings in Some Families of Digraphs

Abstract

The purpose of this paper is to find fault-tolerant fixed routings in some families of digraphs that have been widely considered into the design of interconnection networks. A routing $\rho$ in a digraph G assigns to each pair of vertices a fixed path (called a route) between them. For a given set of faulty vertices and/or arcs, the vertices of the surviving route digraph are the nonfaulty vertices and there is an arc between two vertices if and only if there are no faults on the route between them. The diameter of the surviving route digraph measures the fault tolerance of the routing. In this work, sufficient conditions are found for a digraph to have a routing such that for any set of faults with a bounded number of elements the diameter of the surviving route digraph is at most 3. These results are applied to prove the existence of routings with this property in the generalized de Bruijn and Kautz digraphs, the bipartite digraphs BD(d,n), and general iterated line digraphs.