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Maximizing the sum capacity in the multiple-input multiple-output (MIMO) broadcast channel requires the use of dirty paper coding (DPC). However, practical implementations of DPC which are nearly optimum exhibit high computational complexity. As an alternative to DPC linear zero-forcing can be used where the multiuser interference is completely canceled by linear beamforming. Determining the optimum user allocation, transmit and receive filters thereby constitutes a combinatorial and nonconvex optimization problem. To circumvent its direct solution and therefore reduce complexity, we propose an algorithm that successively allocates data streams to users and, in contrast to state-of-the-art approaches, includes the receive filters into the optimization. We then show several steps that reduce the complexity of the algorithm at marginal performance losses. Thus, performance of state-of-the-art approaches can be maintained while the computational complexity is reduced considerably, as it is shown by a detailed complexity analysis and simulation results.