Truly distribution-independent algorithms for the N-body problem
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. 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.
- Authors:
- Publication Date:
- Research Org.:
- Ames Lab., Ames, IA (United States)
- Sponsoring Org.:
- USDOE, Washington, DC (United States)
- OSTI Identifier:
- 10161854
- Report Number(s):
- IS-M-789; CONF-941118-4
ON: DE94014238
- DOE Contract Number:
- W-7405-ENG-82
- Resource Type:
- Conference
- 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
- Subject:
- 97 MATHEMATICS AND COMPUTING; MANY-BODY PROBLEM; ALGORITHMS; DISTRIBUTION; SIMULATION; 990200; MATHEMATICS AND COMPUTERS
Citation Formats
Aluru, Srinivas, Prabhu, G. M., and Gustafson, John. Truly distribution-independent algorithms for the N-body problem. United States: N. p., 1994.
Web. doi:10.1109/SUPERC.1994.344305.
Aluru, Srinivas, Prabhu, G. M., & Gustafson, John. Truly distribution-independent algorithms for the N-body problem. United States. https://doi.org/10.1109/SUPERC.1994.344305
Aluru, Srinivas, Prabhu, G. M., and Gustafson, John. 1994.
"Truly distribution-independent algorithms for the N-body problem". United States. https://doi.org/10.1109/SUPERC.1994.344305. https://www.osti.gov/servlets/purl/10161854.
@article{osti_10161854,
title = {Truly distribution-independent algorithms for the N-body problem},
author = {Aluru, Srinivas and Prabhu, G. M. and Gustafson, John},
abstractNote = {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.},
doi = {10.1109/SUPERC.1994.344305},
url = {https://www.osti.gov/biblio/10161854},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 1994},
month = {Tue Nov 01 00:00:00 EST 1994}
}