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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Near-optimal density estimation in near-linear time using variable-width histograms Given a univariate distribution with support on the unit interval, this paper develops a method for estimating the density of the distribution via a histogram. The histogram has the following features: the bins are data-dependent, the bins are determined efficiently (near linear time), the number of bins k is specified by the user, and the estimator satisfies a probably approximately correct type performance guarantee. The paper is entirely theoretical. Pros: The writing is clear.