Fast transmission among many sources and destinations usually has the goal of minimizing some objective (such as cost) while satisfying some constraints such as delay or bandwidth. Due to these constraints, the solution sometimes is achieved only through the use of multiple-shared multicast trees (MSMT), which use more than one multicast tree to serve multiple sources and destinations. Minimizing the number of multiple-shared multicast trees, however, has been proven to be NP-complete. In this paper we propose three algorithms for this problem and compare them with an existing one. We can prove, theoretically and through simulations, that our algorithms gives the same good results with a significantly shorter run-time. On the other hand, fast transmission and high reliability are also achieved by selecting the path with large bandwidth. We apply the MBDC (maximum bottleneck bandwidth with delay constraint) algorithm, which we previously proposed, to the MSMT algorithms to optimize them in terms of bandwidth. Proof of correctness, estimation of run-time, and simulation results of these extensions are also provided.
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