Abstruct-Express cubes are 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 independent 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. Express channels may be inserted into existing interconnection networks using interchanges. No changes to the local communication controllers are required.Index Terms-Communication networks, concurrent computing, interconnection networks, multicomputers, packet routing, packet switching, parallel processing, topology. An interconnection network is characterized by its topology, routing, and flow control [lo]. The topology of a network is the arrangement of its nodes and channels into a graph. Routing determines the path chosen by a message in this graph. Flow control deals with the allocation of channel and buffer resources to a message as it travels along this path. This paper deals only with topology. Express cubes can be applied independent of routing and flow control strategies. The performance of a network is measured in terms of its latency and its throughput. The latency of a message is the elapsed time from when the message send is initiated until the message is completely received. Network latency is the average message latency under specified conditions. Network throughput is the number of messages the network can deliver per unit time. Low-dimensional k-ary n-cube networks using wormhole routing have been shown to provide low latency and high throughput for networks that are wire-limited [4], [5], [9]. For n 3, the k-ary n-cube topology is wire-efficient in that it makes efficient use of the available bisection width. This topology maps into the three physical dimensions in a manner that allows messages to use all of the available bandwidth along their path without ever having to double back on themselves. Also, low-dimensional k-ary n-cubes concentrate bandwidth into a few wide channels so that the component of latency due to message length is reduced. In most contemporary concurrent computers, this is the dominant component of latency. Because of their low-latency, high throughput, and affinity for implementation in VLSI, these k-ary n-cube networks with n = 2 or 3 have been used However, low-dimensional k-ary n-cube intercon...