Optimal broadcasting on incomplete star graph interconnection networks

Broadcasting is an important collective communication operation in many applications which use parallel computing. In this paper, we focus on designing broadcasting algorithms for general incomplete star graphs. We propose two optimal one-to-all broadcasting algorithms for incomplete star graphs with a single-port communication model. An incomplete star graph with N nodes, where (n − 1)! < N < n!, is a subgraph of an n-dimensional star graph. The first scheme is single-message one-to-all broadcasting that takes O(n log n) steps. The second one is multi-message one-to-all broadcasting that takes O(n log n + m) steps.