An optimal message routing algorithm for circulant networks

Authors:
Tomaž Dobravec;Janez Žerovnik;Borut Robič
Affiliations:
Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia;Faculty of Mechanical Engineering, University of Maribor, Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia;Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia
Venue:
Journal of Systems Architecture: the EUROMICRO Journal
Year:
2006

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Abstract

A k-circulant network G(n; h1, h2,..., hk) is an undirected graph where the node set is Zn = {0, 1,..., n - 1} and the edge set is the union of sets of unordered pairs Ei = {(u,u + sign(i) * h|i|(mod n)) |u ∈ Zn}, for i ∈ {-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.