Cyclic networks: A family of versatile fixed-degree interconnection architectures

In this paper, we propose a new family of interconnection networks, called cyclic networks (CNs), in which an intercluster connection is defined on a set of nodes whose addresses are cyclic shifts of one another. The node degrees of basic CNs are independent of system size, but can vary from a small constant (e.g., 3) to as large as required, thus providing flexibility and effective tradeoff between cost and performance. The diameters of suitably constructed CNs can be asymptotically optimal within their lower bounds, given the degrees. We show that packet routing and ascend/descend algorithms can be performed in Θ(log_d N) communication steps on some CNs with N nodes of degree Θ(d). Moreover CNs can also efficiently emulate homogeneous product networks (e.g., hypercubes and high dimensional meshes). As a consequence, we obtain a variety of efficient algorithms on such networks, thus proving the versatility of CNs