We focus on throughput-maximizing, max-min fair, and proportionally fair scheduling problems for centralized cognitive radio networks. First, we propose a polynomial-time algorithm for the throughput-maximizing scheduling problem. We then elaborate on certain special cases of this problem and explore their combinatorial properties. Second, we prove that the max-min fair scheduling problem is NP-Hard in the strong sense. We also prove that the problem cannot be approximated within any constant factor better than 2 unless P=NP. Additionally, we propose an approximation algorithm for the max-min fair scheduling problem with approximation ratio depending on the ratio of the maximum possible data rate to the minimum possible data rate of a secondary users. We then focus on the combinatorial properties of certain special cases and investigate their relation with various problems such as the multiple-knapsack, matching, terminal assignment, and Santa Claus problems. We then prove that the proportionally fair scheduling problem is NP-Hard in the strong sense and inapproximable within any additive constant less than log(4/3). Finally, we evaluate the performance of our approximation algorithm for the max-min fair scheduling problem via simulations. This approach sheds light on the complexity and combinatorial properties of these scheduling problems, which have high practical importance in centralized cognitive radio networks.