Broadcast is an important collective communication for either users’ programs or the underlying high-performance computing platforms. In this paper, we present a hierarchical method for broadcast over clusters of SMPs (CSMPs) connected by switches under the one-port model. A broadcast over CSMPs consists of three levels, one for a sub-broadcast in each SMP node, one for a sub-broadcast within each of switches called intra-switch broadcast, and one for a sub-broadcast among switches called interswitch broadcast. Regarding high-performance of switches, our concern focuses on interswitch broadcasts. The new inter-switch broadcast is based on Single-Source Shortest path Minimum-cost Spanning Tree (SSS-MST). In general, a broadcast over an SSSMST may not outperform due to sequential effects arisen from poor usage of bandwidth per link and nodes having receiving broadcasted messages under the one-port model. In our new algorithm, we obtain the optimal concurrency in each step of broadcasts such that as many messages as possible are forwarded simultaneously in each step of SSSMST with the optimal number of steps and minimum cost. The two heuristics, from-upto-down and from-down-to-up algorithms, are proposed to obtain this maximum concurrency using the static topological information and costs for links. Additionally, for regular programs a local update technique is applied to adapt to the dynamic changes in topology and available bandwidth per link over the underlying interconnects.