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Diagonal and Toroidal Mesh Networks
July 1994 (vol. 43 no. 7)
pp. 815-826

Diagonal and toroidal mesh are degree-4 point to point interconnection models suitable for connecting communication 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/spl times/71=2485, N=49/spl times/99=4851, and N=69/spl times/139=9591 nodes under a constant system with a fixed number of messages. 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.

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Index Terms:
hypercube networks; performance evaluation; network routing; toroidal mesh networks; diagonal mesh networks; degree-4 point to point interconnection models; parallel computers; multicomputers; wirability; scalability; optimal self-routing algorithm; performance; deflection routing.
K.W. Tang, S.A. Padubidri, "Diagonal and Toroidal Mesh Networks," IEEE Transactions on Computers, vol. 43, no. 7, pp. 815-826, July 1994, doi:10.1109/12.293260
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