We consider the user selection downlink MU-MIMO scheduling problem in the practical case where there are more users than transmit antennas. First, we deduce a number of structural properties for the sum data rate maximization function under the reduced-complexity suboptimal approaches of zeroforcing dirty-paper (ZF-DP) and zero-forcing beamforming (ZFBF) precoding. Next, we take advantage of the algorithmic literature proposed in the context of combinatorial auctions when bidders have subadditive valuations and propose a novel, fast, greedy approach with very low computational complexity. Then, we establish that both the proposed greedy algorithm and a previously proposed algorithm, which iteratively augments the scheduled user set, attain a M-approximation factor for both ZF-BF and ZF-DP precodings, where M is the number of antennas. To the best of our knowledge, this is the first time that non-asymptotic performance bounds are obtained for this problem. Finally, we compare via simulations the average sum rates achieved by the greedy algorithms with the capacity of the channel and show that they all achieve the full multiplexing gain and their performance is not far from the optimal.