Consider a channel allocation problem over a frequency-selective channel. There are K channels (frequency-bands) and N users such that K = bN for some positive integer b. We want to allocate b channels (or resource blocks) for each user. Due to the nature of the frequency-selective channel, each user considers some channels to be better than others. Allocating each user only good channels will result in better performance than an allocation that ignores the selectivity of the channel. The optimal solution for this resource allocation problem can be computed using the Hungarian algorithm. However, this requires knowledge of the numerical value of all the channel gains, which makes this approach impractical for large networks. We suggest a suboptimal approach, that only requires knowing what the M-best channels of each user are. We find the minimal value of M such that there exists an allocation where all the b channels each user gets are among his M-best. This leads to a feedback of significantly less than one bit per user per channel. For a large class of fading distributions, including Rayleigh, Rician, m-Nakagami and more, this suboptimal approach leads to both an asymptotically (in K) optimal sum-rate and asymptotically optimal minimal rate. Our non-opportunistic approach achieves asymptotically full multiuser diversity and optimal fairness, in contrast to all existing limited feedback algorithms.