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We consider the scheduling and power control problem for spectrum sharing between secondary users and primary users in a spatial reuse time-division multiple access (STDMA) network. The objective is to minimize the transmission length of secondary users in a frame subject to the interference constraints for primary users and the traffic demand of secondary users. The uncertainty of the channel gains is taken into account. Since the power allocation can be improper with respect to the link gain realization, transmissions in the secondary links may fail, and hence, require more time slots. Therefore, traffic demand uncertainty resulting from channel gain variation is also considered. We propose an efficient algorithm based on column generation for robust optimal scheduling and power control for secondary users in presence of channel gain and traffic demand uncertainty. Numerical results show that the proposed algorithm has high computation speed with very low penalty cost when compared to the optimal algorithm. By adjusting the degree of conservatism, we can balance the tradeoff between the robustness and the transmission length of secondary users in a frame.