An optimal message routing algorithm for circulant networks

摘要

A k-circulant network G(n;h(1),h(2),....h(k)) is an undirected graph where the node set is Z(n)={0.1,...,n-1}and the edge set is the union of sets of unordered pairs E-i={(u,u+sign(i) * h(vertical bar i vertical bar)(mod n))vertical bar u is an element of Z(n)}, for i is an element of {-k,...,-1, 1,...,k}. We present an optimal (i.e. using shortest paths) dynamic two-terminal message routing algorithm for k-circulant networks, k >= 2. Instead of computing the shortest paths in advance or using routing tables, our algorithm uses only the address of the final destination to determine the next node to which the message must be sent in order to stay on one of the shortest paths to its destination. We introduce the restricted shortest paths, which are used by Our routing algorithm, and present an efficient algorithm for their construction in 2-circulant graphs. (C) 2006 Elsevier B.V. All rights reserved.