Computing Spatial Distance Histograms Efficiently in Scientific Databases

Particle simulation has become an important research tool in many scientific and engineering fields. Data ge nerated by such simulations impose great challenges to datab se storage and query processing. One of the queries against par ticle simulation data, the spatial distance histogram (SDH) quer y, 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 eas ily implemented by augmenting a Quad-tree index. We also show th e results of rigorous mathematical analysis of the time compl exity of the proposed algorithm: our algorithm runs on Θ(N 3 2 ) for two-dimensional data and Θ(N 5 3 ) for three-dimensional data, respectively. We also propose an approximate SDH processin g algorithm whose running time is unrelated to the input sizeN . Experimental results confirm our analysis and show that the approximate SDH algorithm achieves very high accuracy.