Computing Distance Histograms Ef?ciently in Scientific Databases

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. In this paper, we propose a novel algorithm to compute SDH based on a data structure called density map, which can be easily implemented by augmenting a quad-tree index. We also show the results of rigorous mathematical analysis of the time complexity of the proposed algorithm: our algorithm runs on ominus(N^3/2) for two-dimensional data and ominus(N^5/3) for three-dimensional data, respectively. We also propose an approximate SDH processing algorithm whose running time is unrelated to the input size N. Experimental results confirm our analysis and show that the approximate SDH algorithm achieves very high accuracy.