Broadcasting on incomplete star graph interconnection networks

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 by K. Qiu (1995) to broadcast them.