Broadcasting Algorithms for the Star-Connected Cycles Interconnection Network

Abstract

The star-connected cycles (SCC) graph was recently proposed as an alternative to the cube-connected cycles (CCC) graph, using a star graph to connect cycles of nodes rather than a hypercube. This paper presents an analysis of broadcasting algorithms for SIMD and MIMD SCCs, covering both one-port and multiple-port versions. We show that O(n log n) one-port broadcasting algorithms that have been proposed for the n-star cannot be efficiently extended to the case of the n-SCC graph. However, a simple but rather inefficient algorithm requiring O(n2) steps in the n-star graph can run in O(n) time in the n-SCC if a proper combination of parallelism and transmission rates in the links connecting the nodes is selected. The result is that broadcasting in the n-SCC can be accomplished efficiently, requiring a running time better than or equal to that of an n-star containing (n − 1) times fewer nodes.