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Nearest Neighbor Trees and N-body Simulation

In this paper, we study data structures for N-body simulation. The basic data structure is a hierarchical partition of the input which is used for clustering particles in order to perform an eecient force computation. We are interested in Nearest Neighbor Trees which are formed by repeatedly combining mutually closest pairs of points to create a binary tree. This data structure is an alternative to the more commonly used oct-tree structure, and may be advantageous in practice. In this paper, our goal is to establish a theoretical basis to support the use of Nearest Neighbor Trees. Our main result is to prove that Strict Nearest Neighbor Trees satisfy a logarithmic height bound.