This paper focuses on an important query in scientific simulation data analysis: the Spatial Distance Histogram (SDH). The computation time of an SDH query using brute force method is quadratic. Often, such queries are executed continuously over certain time periods, increasing the computation time. We propose highly efficient approximate algorithm to compute SDH over consecutive time periods with provable error bounds. The key idea of our algorithm is to derive statistical distribution of distances from the spatial and temporal characteristics of particles. Upon organizing the data into a Quad-tree based structure, the spatiotemporal characteristics of particles in each node of the tree are acquired to determine the particles' spatial distribution as well as their temporal locality in consecutive time periods. We report our efforts in implementing and optimizing the above algorithm in graphics processing units (GPUs) as means to further improve the efficiency. The accuracy and efficiency of the proposed algorithm is backed by mathematical analysis and results of extensive experiments using data generated from real simulation studies.

中文翻译：

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即时计算大型科学数据集的空间距离直方图

本文重点介绍科学模拟数据分析中的一个重要查询：空间距离直方图（SDH）。使用蛮力方法的 SDH 查询的计算时间是二次的。通常，此类查询会在特定时间段内连续执行，从而增加了计算时间。我们提出了高效的近似算法来计算具有可证明误差界限的连续时间段的 SDH。我们算法的关键思想是从粒子的空间和时间特征推导出距离的统计分布。在将数据组织成基于四叉树的结构后，获取树的每个节点中粒子的时空特征，以确定粒子在连续时间段内的空间分布及其时间局部性。我们报告了我们在图形处理单元 (GPU) 中实现和优化上述算法的努力，以进一步提高效率。所提出算法的准确性和效率得到了数学分析和使用真实模拟研究产生的数据的广泛实验结果的支持。