Multicast sessions may have a large number of receivers with heterogeneous reception capacities. To accommodate this heterogeneity, various multi-rate schemes, based upon the use of layering or replication, have been proposed. We consider in this paper the optimal partitioning of receivers into groups for multi-rate schemes. For a general class of utility functions, we formulate the partitioning problem as an optimization problem to maximize the sum of receiver utilities. We present an efficient dynamic programming algorithm to solve the partitioning problem, and prove that the solution it finds is optimal. We also show that the majority of the benefit of a multi-rate scheme can be gained by using a small number of groups (or layers), say 4 to 5. To illustrate our solution approach, we apply it to the case where receiver capacities are determined by multi-rate max-min fair rates. A complete protocol for receiver rates computation, rates collection, optimal receiver partitioning, and receiver adaptation is presented. We then compare our approach with other multi-rate approaches as well as a single-rate approach. Experimental results show that our approach provides substantial performance improvements. 1
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