Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. Previous work has developed efficient algorithms that compute exact SDHs. While beating the naive solution, such algorithms are still not practical in processing SDH queries against large-scale simulation data. In this paper, we take a different path to tackle this problem by focusing on approximate algorithms with provable error bounds. We first present a solution derived from the aforementioned exact SDH algorithm, and this solution has running time that is unrelated to the system size N. We also develop a mathematical model to analyze the mechanism that leads to errors in the basic approximate algorithm. Our model provides insights on how the algorithm can be improved to achieve higher accuracy and efficiency. Such insights give rise to a new approximate algorithm with improved time/accuracy tradeoff. Experimental results confirm our analysis.

中文翻译：

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计算具有精度保证的空间距离直方图的近似算法

粒子模拟已成为许多科学和工程领域的重要研究工具。此类模拟生成的数据对数据库存储和查询处理提出了巨大挑战。对粒子模拟数据的查询之一，空间距离直方图 (SDH) 查询，是许多高级分析的构建块，需要二次时间才能使用简单的算法进行计算。以前的工作已经开发出计算精确 SDH 的有效算法。虽然击败了朴素的解决方案，但这种算法在处理针对大规模模拟数据的 SDH 查询时仍然不切实际。在本文中，我们通过关注具有可证明误差界限的近似算法，采取不同的途径来解决这个问题。我们首先提出从上述精确 SDH 算法导出的解决方案，并且该解决方案的运行时间与系统大小N无关。我们还开发了一个数学模型来分析导致基本近似算法错误的机制。我们的模型提供了有关如何改进算法以实现更高准确性和效率的见解。这些见解产生了一种新的近似算法，具有改进的时间/精度权衡。实验结果证实了我们的分析。