On three-stage interconnection networks for group communications

This paper presents an improved three-stage polygonal switching network (PSN) for group communications. We develop a job scheduling based switch box design scheme for hyper-universal switch boxes of k sides and W terminals on each side ((k, W)-HUSBs). Applying this scheme we design a (k, W)-HUSB with k² (k - 1)W switches, and consequently an (n¹3/, n²3/)-HUSB with O(n⁵3/) switches. Putting such a (n¹3/, n²3/)-HUSB at the middle stage and n¹3/ full n²3/ × n²3/ crossbars at the first and third stages joining n ports, we obtain a PSN of O(n⁵3/) switches capable of realizing every group communication requirement.