Donald Bren School of Information and Computer Sciences

Orthogonal graphs were introduced as a simple but powerful tool for the description and analysis of a class of interconnection networks. Routing, and hence finding shortest paths between any two nodes of an orthogonal graph, becomes an important problem. It is shown in this paper that routing in this class of graphs reduces to a node covering problem in the bipartite coverage graph of the orthogonal graph. A minimum cover clearly leads to a shortest path. In general, the problem of finding the mínimum node cover in a bipartite graph is NP-complete. However, the bipartite coverage graphs corresponding to orthogonal graphs have a regular pattern of edges. This allows the development of a routing algorithm which results in a minimum cover. The procedure executes in polynomial time in the number of bit-nodes of the bipartite graph. It therefore results in a shortest path algorithm whose time complexity is quadratic in the logarithm of the number of nodes in the original orthogonal graph.