Circuit-Switched Broadcasting in Multi-port Multi-dimensional Torus Networks

This paper studies the one-to-all broadcast problem in a circuit-switched torus with α-port capability, where a node can simultaneously send and receive α messages at one time. We show how to efficiently perform broadcast in 2-D and 3-D tori of any size, square or non-square, using near optimal numbers of steps. The main techniques used are: (i) a “span-by-dimension” approach, which makes our solution scalable to torus dimensions, and (ii) a “squeeze-then-expand” approach, which makes possible solving the difficult cases where tori are non-square. Existing results, as compared to ours, can only solve very restricted sizes or dimensions of tori, or use more numbers of steps.