Abstract
In this paper we present efficient dynamic algorithms for approximation of k th, 1 ≤ k ≤ \( \left( \begin{gathered} n \hfill \\ 2 \hfill \\ \end{gathered} \right) \) 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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Bespamyatnikh, S., Segal, M. (2003). Dynamic Algorithms for Approximating Interdistances. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_89
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DOI: https://doi.org/10.1007/3-540-45061-0_89
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