### Abstract

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(n^{2}) 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 processor CREWPR AM. 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.

Original language | English (US) |
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Title of host publication | Computing and Combinatorics - 4th Annual International Conference COCOON 1998, Proceedings |

Editors | Wen-Lian Hsu, Ming-Yang Kao |

Publisher | Springer Verlag |

Pages | 95-104 |

Number of pages | 10 |

ISBN (Print) | 3540648240, 9783540648246 |

State | Published - Jan 1 1998 |

Externally published | Yes |

Event | 4th Annual International Computing and Combinatorics Conference, COCOON 1998 - Taipei, Taiwan, Province of China Duration: Aug 12 1998 → Aug 14 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1449 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th Annual International Computing and Combinatorics Conference, COCOON 1998 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 8/12/98 → 8/14/98 |

### Keywords

- Cost optimal algorithms
- Force field evaluation
- N-body simulations
- PRAM
- Paralle algorithms
- Spatial tree data structures

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Computing and Combinatorics - 4th Annual International Conference COCOON 1998, Proceedings*(pp. 95-104). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1449). Springer Verlag.