Streaming Algorithms for Halo Finders

Cosmological N-body simulations are essential for studies of the large-scale distribution of matter and galaxies in the Universe. This analysis often involves finding clusters of particles and retrieving their properties. Detecting such "halos" among a very large set of particles is a computationally intensive problem, usually executed on the same super-computers that produced the simulations, requiring huge amounts of memory. Recently, a new area of computer science emerged. This area, called streaming algorithms, provides new theoretical methods to compute data analytics in a scalable way using only a single pass over a data sets and logarithmic memory. The main contribution of this paper is a novel connection between the N-body simulations and the streaming algorithms. In particular, we investigate a link between halo finders and the problem of finding frequent items (heavy hitters) in a data stream, that should greatly reduce the computational resource requirements, especially the memory needs. Based on this connection, we can build a new halo finder by running efficient heavy hitter algorithms as a black-box. We implement two representatives of the family of heavy hitter algorithms, the Count-Sketch algorithm (CS) and the Pick-and-Drop sampling (PD), and evaluate their accuracy and memory usage. Comparison with other halo-finding algorithms from [1] shows that our halo finder can locate the largest haloes using significantly smaller memory space and with comparable running time. This streaming approach makes it possible to run and analyze extremely large data sets from N-body simulations on a smaller machine, rather than on supercomputers. Our findings demonstrate the connection between the halo search problem and streaming algorithms as a promising initial direction of further research.