Dynamic Algorithms for Approximating Interdistances

In this paper we present efficient dynamic algorithms for approximation of kth, 1 ≤ k ≤ (n 2) distance defined by some pair of points from a given set S of n points in d-dimensional space, for every fixed d. Our technique is based on dynamization of well-separated pair decomposition proposed in [11], computing approximate nearest and farthest neighbors [23,26] and use of persistent search trees [18].

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