Fibonacci circulants-a new interconnection topology

Abstract

The paper proposes a novel interconnection network called Fibonacci circulants for large scale parallel processing systems. The FC(f/sub 3m+2/,3) is a regular and vertex transitive (not edge transitive), and has a Hamiltonian cycle. It connects the (3m+2)-th Fibonacci number, f/sub 3m+2/, m/spl ges/0 nodes with 2m links per node. It is an improvement over a comparable hypercube or multiply-twisted cube that the number of nodes with the same diameter and node degree is (2/sup 2m/)/(f/sub 3m+2/)/spl cong/0.85(0.94)/sup m/. And its diameter and maximum node degree are both 2m, that is two-thirds of a comparable Fibonacci cube with f/sub 3m+2/ processing nodes. The FC(f/sub 3m+2/,3) has a simple routing algorithm, and a Fibonacci tree as a spanning tree.