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As the device shapes keep shrinking, the designs are more sensitive to manufacturing processes. In order to improve performance predictability and yield, mask-layout uniformity/evenness is highly desired, and it is usually measured by the feature densities within defined feasible ranges determined by the manufacturing-process design rules. To address the density-control problem, one fundamental problem is how to calculate density accurately and efficiently. In this paper, we propose a fast exact algorithm to identify the maximum/minimum density for a given layout. Compared with the existing exact algorithms, our algorithm reduces the running time from days/long hours to a few minutes/seconds. Moreover, it is even faster than the existing approximate algorithms in the literature.