Distribution-Independent Hierarchical Algorithmsfor the N-body Problem

Authors:
Srinivas Aluru;John Gustafson;G. M. Prabhu;Fatih E. Sevilgen
Affiliations:
Dept. of CS, New Mexico State University, Email: aluru@cs.nmsu.edu;Scalable Computing Laboratory, Ames Laboratory, Iowa State University, Email: gus@scl.ameslab.gov;Dept. of CS, Iowa State University, Email: prabhu@cs.iastate.edu;Dept. of EECS, Syracuse University, Email: sevilgen@top.cis.syr.edu
Venue:
The Journal of Supercomputing
Year:
1998

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Abstract

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. Greengards 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 thatGreengards algorithm is distribution dependent and has a lower bound of (N log 2 N) in two dimensions and (N log 4 N) in three dimensions. We analyze the Greengard and Barnes-Hut algorithms and show that they are unbounded for arbitrary distributions. We also present a truly distribution independent algorithm for the N-body problem that runs in O(N log N) time for any fixed dimension.