A Cost Optimal Parallel Algorithm for Computing Force Field in N-Body Simulations

  • Guoliang Xue
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)


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 n log n 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.


Paralle algorithms spatial tree data structures force field evaluation N-body simulations PRAM cost optimal algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Guoliang Xue
    • 1
  1. 1.Department of Computer ScienceThe University of VermontBurlingtonUSA

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