A fast algorithm for particle simulations
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
Astrophysical N-body simulations using hierarchical tree data structures
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
A parallel hashed Oct-Tree N-body algorithm
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Journal of Parallel and Distributed Computing
Greengard's N-Body Algorithm is Not Order N
SIAM Journal on Scientific Computing
An O(n) time hierarchical tree algorithm for computing force field in n-body simulations
Theoretical Computer Science
Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters
Journal of Global Optimization
Scalable parallel formulations of the barnes-hut method for n-body simulations
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Tree data structures for N-body simulation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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We consider the following force field computation problem: given a cluster of n particles in 3-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n(n-1)/2 pairs, direct method requires Θ(n2) time for force-evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous Θ(n log n) time hierarchical tree algorithms were published by Appel [3] and by Barnes and Hut [4] respectively. In a recent paper, we presented a linear time algorithm which builds the oct tree bottom-up and showed that Appel's algorithm can be implemented in Θ(n) sequential time. In this paper, we present an algorithm which computes the force field in Θ(log n) time using an n/log n processor CREW PRAM. A key to this optimal parallel algorithm is replacing a recursive top-down force calculation procedure of Appel by an equivalent non-recursive bottom-up procedure. Our parallel algorithm also yields a new Θ(n) time sequential algorithm for force field computation.