In this paper, we study the problem of the SUM query approximation with histograms. We define a new kind of histogram called the SUM-optimal histogram which can provide better estimation result for the SUM queries than the traditional equi-depth and V-optimal histograms. We propose three methods for the histogram construction. The first one is a dynamic programming method, and the other two are approximate methods. We use a greedy strategy to insert separators into a histogram and use the stochastic gradient descent method to improve the accuracy of separators. The experimental results indicate that our method can provide better estimations for the SUM queries than the equi-depth and V-optimal histograms.

中文翻译：

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SUM最佳直方图用于近似查询处理

在本文中，我们研究使用直方图的SUM查询近似问题。我们定义了一种新的直方图，称为SUM最优直方图，与传统的等深度和V最优直方图相比，它可以为SUM查询提供更好的估计结果。我们提出了三种直方图构造方法。第一个是动态编程方法，另外两个是近似方法。我们使用贪婪策略将分隔符插入直方图中，并使用随机梯度下降方法提高分隔符的准确性。实验结果表明，与等深度和V最优直方图相比，我们的方法可以为SUM查询提供更好的估计。