Broadcasting in (n,k)-Arrangement Graph Based on an Optimal Spanning Tree

The tree structure has received much interest as a versatile architecture for a large class of parallel processing applications. Spanning trees in particular are essential tools for some important communication problems such as broadcasting and personalized communications. When it refers to communications, it always involves two costs. Specifically, sending a packet of b bytes along a link takes T _s + bT_c time, where T_s is the time to initialize (or start-up) the communication link and T_c is the latency to transmit a byte. To optimize these costs, a spanning tree is constructed to solve one-to-all broadcasting problem in an (n, k)-arrangement graph. Since the spanning tree has an optimal height, our algorithm achieves optimal start-up cost O(D(A_n,k))T_s and transmission cost O((m/k(n-k))T_c) under the all-port model, and optimal transmission cost O(mT_c) under the one-port model