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Existing capacity constrained cellular networks that operate in fixed spectrum bands can be enhanced with capacity-on-demand services using the Coordinated Dynamic Spectrum Access (CDSA) model. In this model, a centralized spectrum broker coordinates access to spectrum in a given region and assigns short term spectrum leases to competing wireless service providers and/or end users. In contrast to existing multi-year cellular spectrum licenses that span large regions, a spectrum broker can grant spectrum leases that are for small regions (e.g.: per base station) and valid for short durations (e.g.: tens of minutes). Fast spectrum allocation algorithms are crucial to the design of scalable spectrum brokers that can provide such realtime spectrum access. In this paper, we address this challenge. Specifically, we formulate the spectrum allocation problem as two optimization problems: first with the objective of maximizing the overall demand (Max-Demand) satisfied among the various base stations and the second with the objective of minimizing the overall interference in the network (Min-Interference) when all the demands of the base stations are satisfied. We show that the optimization problems are NP-hard and design efficient algorithms to solve them. Our simulation results on sample network topologies show that our algorithms scale very well for large network sizes.