Many-to-many multicast routing can be extensively applied in computer or communication networks supporting various continuous multimedia applications. The paper focuses on the case where all users share a common communication channel while each user is both a sender and a receiver of messages in multicasting as well as an end user. In this case, the multicast tree appears as a terminal Steiner tree (TeST). The problem of finding a TeST with a quality-of-service (QoS) optimization is frequently NP-hard. However, we discover that it is a good idea to find a many-to-many multicast tree with QoS optimization under a fixed topology. In this paper, we are concerned with three kinds of QoS optimization objectives of multicast tree, that is, the minimum cost, minimum diameter, and maximum reliability. All of three optimization problems are distributed into two types, the centralized and decentralized version. This paper uses the dynamic programming method to devise an exact algorithm, respectively, for the centralized and decentralized versions of each optimization problem.
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