A fast algorithm for particle simulations
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Computational structure of the N-body problem
SIAM Journal on Scientific and Statistical Computing
Vectorization of tree traversals
Journal of Computational Physics
Journal of Computational Physics
A modified tree code: don't laugh; it runs
Journal of Computational Physics
The parallel multipole method on the connection machine
SIAM Journal on Scientific and Statistical Computing
The order of Appel's algorithm
Information Processing Letters
Parallel hierarchical N-body methods
Parallel hierarchical N-body methods
Astrophysical N-body simulations using hierarchical tree data structures
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Parallel hierarchical N-body methods and their implications for multiprocessors
Parallel hierarchical N-body methods and their implications for multiprocessors
A parallel hashed Oct-Tree N-body algorithm
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Journal of Parallel and Distributed Computing
Distribution-independent hierarchical N-body methods
Distribution-independent hierarchical N-body methods
Distribution-Independent Hierarchical Algorithmsfor the N-body Problem
The Journal of Supercomputing
Scalable Parallel Octree Meshing for TeraScale Applications
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Rapid Multipole Graph Drawing on the GPU
Graph Drawing
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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 O(N log N) time in two dimensions and in O(N log2 N) time in three dimensions.