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Histograms are the workhorse of data mining and analysis. This paper considers the problem of publishing histograms under differential privacy, one of the strongest privacy models. Existing differentially private histogram publication schemes have shown that clustering (or grouping) is a promising idea to improve the accuracy of sanitized histograms. However, none of them fully exploits the benefit of clustering. In this paper, we introduce a new clustering framework. It features a sophisticated evaluation of the trade-off between the approximation error due to clustering and the Laplace error due to Laplace noise injected, which is normally overlooked in prior work. In particular, we propose three clustering strategies with different orders of run-time complexities. We prove the superiority of our approach by theoretical utility comparisons with the competitors. Our extensive experiments over various standard real-life and …