Adjusting Parameters of k-Ary n-Cube to Achieve Better Cost Performance

The k-ary n-cube, or k-ary n-dimensional torus, is widely used as the interconnection network for constructing commercial supercomputers. Compared to the hypercube, torus has the advantage of ease of implementation but its diameter increases rapidly as the network scales up. This paper investigates the configurations of the k-ary n-cube by adjusting the parameters k and n according to the network size for achieving good cost performance tradeoffs. The node degree and diameter strongly affect the cost performance of the network. An interconnection network consists of routers and links which connect the ports of routers by following up an interconnect topology. The router is commonly implemented with a buffered crossbar switch whose cost increases non-linearly as the number of ports increases. The number of ports in a router is usually larger than the node degree because at least one port is needed to connect the compute node and this port is not counted as part of the node degree. The diameter determines the maximum communication delay between nodes which is a reciprocal proportion to the performance. This paper gives an analytical model for evaluating the relative cost performance (RCP) to hypercube. The model is parameterized with the node degree, the diameter, the router complexity, the number of compute nodes in a node, and the system size. The RCP function for a given n always has a minimum value at a certain system size. This is helpful for us to determine the values of k and n when we design a k-ary n-cube network. We also investigate the k-ary n-dimensional mesh and the unidirectional torus with different parameters. The unidirectional torus has a similar behavior to but better cost performance than the bidirectional torus.