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This paper proposes the first resource allocation scheme in the literature to support scalable-video multicast for WiMAX relay networks. We prove that when the available bandwidth is limited, the bandwidth allocation problems of 1) maximizing network throughput and 2) maximizing the number of satisfied users are NP-hard. To find the near-optimal solutions to this type of maximization problem in polynomial time, this study first proposes a greedy weighted algorithm, GWA, for bandwidth allocation. By incorporating table-consulting mechanisms, the proposed GWA can intelligently avoid redundant bandwidth allocation and thus accomplish high network performance (such as high network throughput or large number of satisfied users). To maintain the high performance gained by GWA and simultaneously improve its worst case performance, this study extends GWA to a bounded version, BGWA, which guarantees that its performance gains are lower bounded. This study shows that the computational complexity of BGWA is also in polynomial time and proves that BGWA can provide at least 1/ρ times the performance of the optimal solution, where rho is a finite value no less than one. Finally, simulation results show that the proposed BGWA bandwidth allocation scheme can effectively achieve different performance objectives with different parameter settings.