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Express Cubes: Improving the Performance of k-ary n-cube Interconnection Networks
September 1991 (vol. 40 no. 9)
pp. 1016-1023

The author discusses express cubes, k-ary n-cube interconnection networks augmented by express channels that provide a short path for nonlocal messages. An express cube combines the logarithmic diameter of a multistage network with the wire-efficiency and ability to exploit locality of a low-dimensional mesh network. The insertion of express channels reduces the network diameter and thus the distance component of network latency. Wire length is increased, allowing networks to operate with latencies that approach the physical speed-of-light limitation rather than being limited by node delays. Express channels increase wire bisection in a manner that allows the bisection to be controlled independently of the choice of radix, dimension, and channel width. By increasing wire bisection to saturate the available wiring media, throughput can be substantially increased. With an express cube both latency and throughput are wire-limited and within a small factor of the physical limit on performance.

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Index Terms:
performance; express cubes; k-ary n-cube; interconnection networks; nonlocal messages; wire bisection; throughput; distributed processing; multiprocessor interconnection networks.
W.J. Dally, "Express Cubes: Improving the Performance of k-ary n-cube Interconnection Networks," IEEE Transactions on Computers, vol. 40, no. 9, pp. 1016-1023, Sept. 1991, doi:10.1109/12.83652
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