Channel-aware scheduling and link adaptation (LA) methods are widely considered to be crucial for realizing high data rates in wireless networks. Multi-carrier systems that spread information bits over the entire signal band can take advantage of the frequency selective fading, and choose the sub-carrier(s) that have the best channel conditions for transmission. However, predicting the future channel states, and adjusting the transmission schedules and parameters accordingly, may consume valuable system resources, such as bandwidth, time, and power. Sub-carrier grouping, which refers to monitoring/treating a set of adjacent sub-carriers as a single unit, has been proposed to reduce the overhead associated with LA. This paper considers various models for sub-carrier grouping, each representing a different level of system complexity, and investigates the trade-offs between the sub-carrier grouping granularity and the link throughput. We first present an offline dynamic programming algorithm for finding an optimal solution, assuming perfect estimates of the channel states. The solution obtained through this formulation can serve as a performance bound for online algorithms. We then propose an online algorithm for the case of perfect channel state estimates, which is shown to have very close performance to the off-line optimal solution. This online algorithm is also extended to incorporate imperfect channel state estimates due to (i) variations in channel states among the sub-carriers within the same group, and (ii) prediction inaccuracies in estimating the future time-slots. Performances of the algorithms are evaluated through simulations and comparisons with the off-line solution. The trade-off between the sub-carrier grouping granularity and the link throughput is also presented. Overall, our results can provide some guidelines from the network scheduling perspective for deciding what kind of sub-carrier grouping model and granularity to use in multi-carrier networks with LA.