KMS-Cube — A general alternative to hypercubes for reducing the node degree

As the scale of parallel computer systems becomes larger year by year, interconnection networks with low node degree and short diameter are required for achieving high communication performance at low cost. This paper presents a general alternative to hypercubes, named KMS-Cube, that keeps interesting topological properties of the hypercube but has a low node degree. A KMS-Cube, denoted by KMSC(k, m, s), is configured with three parameters k, m, and s. The node address has m2k−s + k bits and the node degree is k + m, much less than that of hypercubes. Comparing to other alternatives to hypercubes, KMS-Cube has advantages such as the ease of routing and the flexibility of changing network size. We describe the KMS-Cube's structure and its topological properties, compare it with other networks on the measures of node degree, diameter, and cost ratio, and present an efficient routing algorithm for the KMS-Cube.