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In this paper, we study the multicast routing problem in wireless relay networks. Our objective is to maximize the number of recipients of a multicast stream by deciding the topology of the wireless relay network based on the given resource budget and the channel quality of the nodes. To the best of our knowledge, this important maximization problem has not been previously addressed. Since existing approaches cannot effectively solve the problem, we propose a scheme called multicast subscriber selection (MSS). Through analysis, we prove that the path-construction problem is NP-hard. Our heuristic MSS has polynomial-time complexity, and its performance is bound to the optimal solution. We also evaluate the performance of MSS via simulations. The results demonstrate that the existing unicast routing approach is inefficient under different budgets and channel conditions. In contrast, the proposed MSS scheme achieves better performance, because it can effectively utilize relay stations.