Recursive circulant: a new topology for multicomputer networks (extended abstract)

We propose a new topology for multicomputer networks, called recursive circulant. Recursive circulant G(N, d) is defined to be a circulant graph with N nodes and jumps of powers of d, d/spl ges/2. G(N, d) is node symmetric, has a hamiltonian cycle unless N/spl les/2, and can be recursively constructed when N=cd/sup m/, 1/spl les/c/spl les/d. We analyze various network metrics of G(cd/sup m/, d) such as connectivity, diameter, mean internode distance, visit ratio, and develop a shortest path routing algorithm in G(cd/sup m/, d). G(2/sup m/, 4), whose degree is m, compares favorably to the hypercube Q/sub m/. G(2/sup m/, 4) has the maximum connectivity, and its diameter is [(3m-1)/4]. A simple broadcasting algorithm in G(2/sup m/, 4) is also presented.<>