Dynamic algorithms for approximating interdistances

Authors:
Sergey Bereg;Michael Segal
Affiliations:
Department of Computer Science, University of Texas at Dallas, Box 830688, Richardson, TX;Communication Systems Engineering Department, Ben-Gurion University of Negev, Beer-Sheva 84105, Israel
Venue:
Nordic Journal of Computing
Year:
2004

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Abstract

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. Our technique is based on the dynamization of well-separated pair decomposition proposed in [11], computing approximate nearest and farthest neighbors [22, 25] and use of persistent search trees [17].