Honeycomb networks

Abstract

The honeycomb mesh, based on hexagonal plane tessellation, is considered as a multiprocessor interconnection network. A honeycomb mesh network with n nodes has degree 3 and diameter ≈ 1.63√n -1, which is 25% smaller degree and 18.5% smaller diameter then the mesh connected computer with approximately the same number of nodes. A convenient addressing scheme for nodes is introduced which provides simple computation of shortest paths and the diameter. Simple and optimal (in the number of required communication steps) routing algorithm is developed. Vertex and edge symmetric honeycomb torus network is obtained by adding wrap around edges to the honeycomb mesh. The network cost, defined as the product of degree and diameter, is better for honeycomb networks than for the two other families based on square (mesh connected computers and tori) and triangular (hexagonal meshes and tori) tessellations. The average distance in honeycomb torus with n nodes is proved to be approximately 0.54√n.