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We investigate the problem of finding the linear precoder that maximizes the sum-rate for the vector broadcast channel. In contrast to previous work, we examine the dual uplink problem, where the optimal power allocation must be found. This point of view leads to the observation that considering only uniform power allocations on a user subset yields nearly optimal performance, simplifying the problem to a combinatorial problem. We furthermore present two algorithms with complexity growing only quadratically with the number of users in the system, but with performance comparable to more complex existing schemes.