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We study the robust transmission scheduling and power control problem for spectrum sharing between secondary and primary users in a spatial reuse time-division multiple access (STDMA) network. The objective is to find a robust minimum-length schedule for secondary users (in terms of time slots) subject to the interference constraints for primary users and the traffic demand of secondary users. We consider the fact that power allocation based on average (or estimated) link gains can be improper since actual link gains can be different from the average link gains. Therefore, transmission of the secondary links may fail and require more time slots. We also consider this demand uncertainty arising from channel gain uncertainty. We propose a column generation-based algorithm to solve the scheduling and power control problem for secondary users. The column generation method breaks the problem down to a restricted master problem and a pricing problem. However, the classical column generation method can have convergence problem due to primal degeneracy. We propose an improved column generation algorithm to stabilize and accelerate the column generation procedure by using the perturbation and exact penalty methods. Furthermore, we propose an efficient heuristic algorithm for the pricing problem based on a greedy algorithm. For the simulation scenario considered in this paper, the proposed stabilized column generation algorithm can obtain the optimal schedules with 18.85% reduction of the number of iterations and 0.29% reduction of the number of time slots. Also, the heuristic algorithm can achieve the optimality with 0.39% of cost penalty but 1.67×10-4 times reduction of runtime.