A cost optimal parallel algorithm for computing force field in N-body simulations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


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 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 languageEnglish (US)
Title of host publicationComputing and Combinatorics - 4th Annual International Conference COCOON 1998, Proceedings
EditorsWen-Lian Hsu, Ming-Yang Kao
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540648240, 9783540648246
StatePublished - Jan 1 1998
Externally publishedYes
Event4th Annual International Computing and Combinatorics Conference, COCOON 1998 - Taipei, Taiwan, Province of China
Duration: Aug 12 1998Aug 14 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other4th Annual International Computing and Combinatorics Conference, COCOON 1998
Country/TerritoryTaiwan, Province of China


  • 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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