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Optimal multiuser scheduling which maximizes the sum rate for parallel channel access often involves an NP-hard design problem. In this letter, we propose a low-complexity optimal solution using a two-step procedure: (1) generalized selection multiuser diversity (GSMuD) which ranks the channels of a total of users and selects the users with the largest signal-to-noise ratios (SNRs) for channel access and (2) optimal power allocation for the selected users. Besides the equal power allocation (EPA), two optimal power allocation algorithms for the GSMuD are derived, namely: (1) 1D optimal waterfilling (WF) power allocation along the channels given a fixed total power at each time slot and (2) 2D optimal WF along both the time and the channels given the average total power. Accurate performance analyses of the above schemes are provided. Numerical results show that the 2D WF power allocation yields the highest rate, while the EPA is near-optimal for many cases of practical interest.