Diagonal and Toroidal Mesh Networks

Abstract

Abstract-Diagonal and toroidal mesh are degree-4, point to point interconnection models suitable for connecting communica-tion elements in parallel computers, particularly multicomputers. The two networks have a similar structure. The toroidal mesh is popular and well-studied whereas the diagonal mesh is relatively new. In this paper, we show that the diagonal mesh has a smaller diameter and a larger bisection width. It also retains advantages such as a simple rectangular structure, wirability and scalability of the toroidal mesh network. An optimal self-routing algorithm is developed for these networks. Using this algorithm and the existing routing algorithm for the toroidal mesh, we simulated and compare the performance of these two networks with N = 35 x 71 = 2485, N = 49 x 99 = 4851, and N = 69 x 139 = 9591 nodes under a constant system with a fixed number of mesages. Deflection routing is used to resolve conflicts. The effects of various deflection criteria are also investigated. We show that the diagonal mesh outperforms the toroidal mesh in all cases, and thus provides an attractive alternative to the toroidal mesh network. Index Terms-Massively parallel systems, multicomputers, in-terconnection networks, diameter, bisection width, and deflection routing algorithm. I