The optimization of multicast communication for regular interconnection networks (INs) has been the subject of many studies in the literature. Extensions, however, the analysis of INs with arbitrary topology and background traffic poses a great challenge. In this context, a novel heuristic algorithm for multicast communication is proposed for arbitrary INs with finite capacity and bursty background traffic. The scheme facilitates inter-process communication amongst parallel computers and grid computing networks as well as local and wide area networks and it is applicable to a single-port mode of message passing communication. The scheme utilizes a queue-by-queue decomposition algorithmfor arbitrary open queueing network models, based on the principle of maximum entropy, in conjunction with an information theoretic decomposition criterion and graph theoretic concepts. Evidence based on empirical studies indicates the suitability of the scheme for achieving an optimal multicast communication cost.