Collision-free spatial hash functions for structural analysis of billion-vertex chemical bond networks

State-of-the-art molecular dynamics (MD) simulations generate massive datasets involving billion-vertex chemical bond networks, which makes data mining based on graph algorithms such as K-ring analysis a challenge. This paper proposes an algorithm to improve the efficiency of ring analysis of large graphs, exploiting properties of K-rings and spatial correlations of vertices in the graph. The algorithm uses dual-tree expansion (DTE) and spatial hash-function tagging (SHAFT) to optimize computation and memory access. Numerical tests show nearly perfect linear scaling of the algorithm. Also a parallel implementation of the DTE + SHAFT algorithm achieves high scalability. The algorithm has been successfully employed to analyze large MD simulations involving up to 500 million atoms.