Broadcasting on incomplete star graph interconnection networks

In this paper, we propose two one-to-all optimal broadcasting algorithms in incomplete star graphs. An incomplete star graph with N nodes, where (n - 1)! < N < n!, is a subgraph of an n-star. Using a routing scheme to transmit a message to each substar composed of the incomplete star, our proposed broadcasting algorithm is optimal in O(n log n) on the single-port communication model. While broadcasting m messages on the incomplete star, we also present an optimal algorithm in O(n log n + m). Multi-message broadcasting is done first by transmitting m messages to each substar in a pipelined fashion and then by using the algorithm in [12] to broadcast them.