Abstract
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. © Springer-Verlag Berlin Heidelberg 1999.