This work studies centralized radio resource management in metropolitan area networks with a very large number of access points and user devices. A central controller collects time-averaged traffic and channel conditions from all access points and coordinates spectrum allocation, user association, and power control throughout the network on an appropriate timescale. The timescale is conceived to be seconds in today's networks, and it is likely to become faster in the future. The coordination problem in each time epoch is formulated as a network utility maximization problem, where any subset of access points may use any parts of the spectrum to serve any subsets of devices. It is proved that the network utility can be maximized by an extremely sparse spectrum allocation. By exploiting this sparsity, an efficient iterative algorithm with guaranteed convergence is developed, each iteration of which is performed in closed form. The proposed centralized optimization framework can incorporate a broad class of utility functions that account for weighted sum rates, average packet delay, and/or energy consumption, along with very general constraints on transmission powers. Numerical results demonstrate the feasibility of the algorithm for networks with up to 1,000 access points and several thousand devices. Moreover, the proposed scheme yields significantly improved throughput region and average packet delay comparing with several well-known competing schemes.