A performance comparison of tree data structures for N-body simulation
Journal of Computational Physics
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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 $\Theta(n\log^3n\log L)$ compared with $\Theta(n\log L)$ 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 safe to use tight bounding boxes only for binary decompositions. The results are all directly applicable to practical implementations of N-body algorithms.