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We propose a computationally efficient framework to solve a large class of dynamic coverage and clustering problems, ranging from those that arise from deployment of mobile sensor networks to classification of cellular data for diagnosing cancer stages. This framework provides the ability to identify natural clusters in the underlying data set. In particular, we define the problem of minimizing instantaneous coverage as a combinatorial optimization problem in a Maximum Entropy Principle (MEP) framework that we formulate specifically for the dynamic setting, and which allows us to address inherent tradeoffs such as those between the resolution of the identified clusters and computational cost. The proposed MEP framework addresses both the coverage and the tracking aspects of these problems. Locating cluster centers of swarms of moving objects and tracking them is cast as a control design problem ensuring that the algorithm achieves progressively better coverage with time. Simulation results are presented that highlight the features of this framework; these results demonstrate that the proposed algorithm attains target coverage costs five to seven times faster than related frame-by-frame methods.