Truly distribution-independent algorithms for the N-body problem

The N - body problem is to simulate the motion of N particles under the influence of mutual force fields based on an inverse square law. Greengard's algorithm claims to compute the cumulative force on each particle in O ( N ) time for a fixed precision irrespective of the distribution of the particles. In this paper, we show that Greengard's algorithm is distribution dependent and has a lower bound of ( N log2 N ) in two dimensions and(N log4 N)inthreedimensions. WeanalyzetheGreengard and Barnes-Hut algorithms and show that they are unbounded for arbitrary distributions. We also present a truly distribution independent algorithm for solving the N-body problem inO (N log N ) time in two dimensions and in O (N log 2 N) time in three dimensions.

• Type: Conference
• Year: 1994
• Where: SC
• Authors: Srinivas Aluru, Gurpur M. Prabhu, John L. Gustafson
• Keywords: Algorithm, Applied Computing, Greengard's Algorithm Claims, Mutual Force Fields, SC 1994