Shortest Path Routing and Fault-Tolerant Routing on de Bruijn Networks

this paper, we study the routing problem for the undirected binary de Bruijn interconnection network. Researchers have never proposed a shortest path routing algorithm on the undirected binary de Bruijn network. We first propose a shortest path routing algorithm, whose time complexity in the binary de Bruijn network of 2 m m m nodes is O O O(m m m ). Then, based on our shortest path routing algorithm, we propose two fault-tolerant routing schemes. It is assumed that at most one node fails in the network. In our schemes, two node-disjoint paths are found. Our first fault-tolerant routing algorithm guarantees that one of the two paths is the shortest path, and the other is of length at most m m m + log 2 m m m + 4. Our second algorithm can find two node-disjoint paths with lengths at most m m m and m m m + 4, respectively, if the shortest path is not required in the fault-tolerant routing. 2000 John Wiley & Sons, In

A design for node coloring and 1-fair alternator on de Bruijn networks

In this paper, we study the coloring problem for the undirected binary de Bruijn interconnection network. The coloring scheme is simple and fast. We propose the coloring algorithm by using the pseudo shortestpath spanning tree rooted at 0¡¡¡00. Each processor can find its color number by its own identity. Then, based on our coloring algorithm, we propose a 1-fair alternator. Our design is optimal. In our design, each processor can execute the critical step once in every 3 steps. Key words: alternator; coloring; de Bruijn graph; phase synchronization