Abstract
Each node of a hypercube system, when fabricated, comes with a fixed number of links designed for a maximum sized construction. Very often, there are links left unused at each node in a real system. In this article, we study the hypercube in which extra connections are added between pairs of nodes through otherwise unused links. Those extra connections are made in order to maximize the improvement of the performance measure of interest under various traffic distributions. The resulting hypercube, called the variant hypercube, requires a simple routing algorithm and is guaranteed not to create any traffic-congested point or link. The variant hypercube is found to achieve considerable reduction in diameter, and noticeable improvement in mean internode distance and traffic density. In addition, a variant hypercube is more cost-effective than a regular hypercube and does not suffer from practical implementation difficulty. As a result, it also appears advantageous for hypercube systems with no available unused links to augment each node so as to accommodate an extra link, provided that the building block is not pin limited and is allowed to do so.
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