Properties and performance of the block shift network

As an interconnection network, hypercube topology offers certain advantages such as high data bandwidth and low message latency to achieve computational efficiency. However, a significant drawback of this topology is that the number of ports per node increases with the number of nodes. In addition, in many applications not all the links are used equally frequently, and links on certain dimensions may be idle most of the time during a computation. This suggests that we can provide connections over certain dimensions only to reduce the number of links and can still attain comparable performance. In this paper, we propose a new network, called the Block Shift Network (BSN), for constructing very large multicomputer systems for efficient parallel processing. The network is defined through a pair of parameters and cost and performance of a BSN can be controlled by carefully selecting appropriate parameters defining the network. Actually, many popular networks such as the hypercube, the shuffle-exchange, and the complete networks are instances of the BSN. The topological properties of the BSN with different parameters are analyzed and compared with those of existing popular networks. Basic data movement operations on the BSN are also designed and analyzed. The results show that the BSN with certain parameters can surpasses the hypercube in several respects while retaining most of its advantages, especially when the traffic has the locality property.