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The paper presents a formal study on optimal bandwidth partitioning for multi-rate video broadcasting in a broadband wireless network. The formulation is generic in that it considers both inter-session and intra-session bandwidth partitions for layering as well as stream replication based broadcasting. It also takes into account the most fundamental issues associated with video transmission, including encoding overhead, non-linear relationship between the receiver perceived video quality and the delivered bandwidth, as well as intra-session and inter-session fairness. Specifically, we consider the bandwidth-constrained case with channelized allocation. We show that there exist polynomial time algorithms for both inter-session and intra-session partitioning problems.