Experiences with Parallel N-Body Simulation
IEEE Transactions on Parallel and Distributed Systems
The inverse nearest neighbor problem with astrophysical applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Distribution-Independent Hierarchical Algorithmsfor the N-body Problem
The Journal of Supercomputing
A Cost Optimal Parallel Algorithm for Computing Force Field in N-Body Simulations
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
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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 T(n log3 n log L) compared with T (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.