Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
R.J. Anderson , Dept. of Comput. Sci. & Eng., Washington Univ., Seattle, WA, USA
In this paper, we study data structures for use in N-body simulation. We concentrate on the spatial decomposition tree used in particle-cluster force evaluation algorithms such as the Barnes-Hut algorithm. We prove that a k-d tree is asymptotically inferior to a spatially balanced tree. We show that the worst case complexity of the force evaluation algorithm using a k-d tree is Θ(n log3 n log L) compared with Θ (n log L) for an oct-tree. (L is the separation ratio of the set of points.) We also investigate improving the constant factor of the algorithm, and present several methods which improve over the standard oct-tree decomposition. Finally, we consider whether or not the bounding box of a point set should be "tight", and show that it is only safe to use tight bounding boxes for binary decompositions. The results are all directly applicable to practical implementations of N-body algorithms.
tree data structures; tree data structures; N-body simulation; spatial decomposition tree; particle-cluster force evaluation algorithms; Barnes-Hut algorithm; k-d tree; spatially balanced tree; worst case complexity; force evaluation
R. Anderson, "Tree data structures for N-body simulation," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 224.