Optimal routing in the De Bruijn networks

In this paper, we consider the problem of optimal routing in an interconnection network, called the De Bruijn network, where the sites are linked in the form of a De Bruijn graph. We provide the distance functions for the undirected as well as the directed De Bruijn graphs. The optimal routing problem is then reduced to that of pattern matching. We use Morris and Pratt's failure function and Weiner's prefix tree to develop algorithms that find the shortest paths in the uni-directional and in the bi-directional De Bruijn networks, respectively. These algorithms are linear in time and in space (in the diameter of the graph).