The challenging task of scheduling multi-user orthogonal frequency-division multiplexed transmissions amounts to jointly optimum allocation of subcarriers, rate and power resources. The optimization problem for deterministic channels reduces to an integer program known to be exponentially complex. Interestingly, the present paper shows that almost surely optimal allocation is possible at low complexity in the wireless setup, provided that the random fading channel has continuous distribution function. Specifically, it is established that the ergodic capacity achieving allocation follows a greedy water-filling scheme with linear complexity in the number of users and subcarriers. The result extends to accommodate fairness through general utility functions and constraints on the minimum average user rates. When the channel distribution is known, the optimal on-line scheme relies on low-complexity provably convergent subgradient iterations to obtain pertinent dual variables off line. To accommodate channel uncertainties, stochastic subgradient iterations provide dual variables on line with guaranteed convergence to their off-line counterparts.