Diagonal and Toroidal Mesh Networks

Ah&z&-Diagonal and toroidal mesh are degree-4, point to point intercoimection models suitable for connecting communication elements in parallel computers, particularly multicomputers. The two networks have a similar structure. The toroidai mesh is popular and well-studied whereas tbe 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 scalabiity of tbe toroidal mesh network. An optimal selfrouting algorithm is developed for these networks. Using tbis algorithm and tbe existing routing algorithm for the toroidal mesh, we simulated and compare tbe 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 messages. Deflection routing is used to resolve conflicts. Tbe effects of various deflection criteria are also investigated. We show that tbe diagonal mesh outperforms the toroidal mesh in all cases, and thus provides an attractive alternative to the toroidal mesh network.