Bounded-Error Compression of Particle Data from Hierarchical Approximate Methods

This paper presents an analytical and computational framework for the compression of particle data resulting from hierarchical approximate treecodes such as the Barnes-Hut and Fast Multipole Methods. Due to the approximations introduced by hierarchical methods, the position (as well as velocity and acceleration) of a particle can be bounded by a distortion radius. We develop storage schemes that maintain this distortion radii while maximizing compression. Our schemes make extensive use of spatial and temporal coherence of particle behavior and yield compression ratios higher than 12:1 over raw data, and 6:1 over gzipped (LZ78) raw data. We demonstrate that for uniform distributions with 100K particles, storage requirements can be reduced from 1200KB (100K × 12B) to about 99KB (under 1 byte per particle per timestep). This is significant because it enables faster storage/retrieval, better temporal resolution, and improved analysis. Our results are shown to scale from small systems (2K particles) to much larger systems (over 100K particles). The associated algorithm is optimal (O(n)) in both storage and computation with small constants.