Modern cellular base stations can transmit over multiple frequencies, and further choose to transmit to different users over different frequencies. In much of the prior literature, it is assumed that the channel state of each user over each frequency is known. However, to get such channel state information for each user-channel pair requires a large overhead. Here, we consider the problem of computationally efficient and throughput-optimal scheduling in networks where the base station ensures a

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... small probing overhead by limiting the number of allowed probe packets per time slot. We first argue that a naive optimizationbased MaxWeight algorithm is combinatorially infeasible to implement, and then design a low-complexity algorithm that achieves the same throughput as the naive MaxWeight algorithm. Through simulations, we also investigate further improvements to achieve very small packet delays.