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 Ω(N log2 N) in two dimensions and Ω(N log4 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 solving the N-body problem in Ω(N log N) time in two dimensions and in Ω(N log2 N) time in three dimensions.
- Research Organization:
- Ames Lab., Ames, IA (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-82
- OSTI ID:
- 10161854
- Report Number(s):
- IS-M-789; CONF-941118-4; ON: DE94014238
- Resource Relation:
- Conference: Supercomputing `94 meeting, Washington, DC (United States), 14-18 Nov 1994; Other Information: PBD: [1994]
- Country of Publication:
- United States
- Language:
- English
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