An optimal fault-tolerant routing algorithm for double-loop networks

A weighted double-loop network can be modeled by a directed graph G(n; h/sub 1/, h/sub 2/; w/sub 1/, w/sub 2/) with vertex set Z/sub n/={0, 1, ..., n-1} and edge set E=E/sub 1//spl cup/E/sub 2/, where E/sub 1/={(u, u+h/sub 1/)|u/spl isin/Z/sub n/}, E/sub 2/={(u, u+h/sub 2/)|u/spl isin/Z/sub n/}. Assume that the weight of each edge in E/sub 1/ is w/sub 1/ and the weight of each edge in E/sub 2/ is w/sub 2/. In this paper, we present an optimal routing algorithm on double-loop networks under the case where there is at most one faulty element. Our algorithm is based on the fact that the shortest path from a vertex to any other vertex in a double-loop network is in the L-shape region.