Dynamic Well-Separated Pair Decomposition Made Easy

نویسندگان

  • John Fischer
  • Sariel Har-Peled
چکیده

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INDEX TERMS: none.

Well-separated pair decomposition, introduced by Callahan and Kosaraju [3], has found numerous applications in solving proximity problems for points in the Euclidean space. A pair of point sets (A, B) is c-well-separated if the distance between A,B is at least c times the diameters of both A and B. A well-separated pair decomposition of a point set consists of a set of well-separated pairs that...

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We present an external memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set P in d in O sort N I/Os using O N B blocks of external memory, where N is the number of points in P, and sort N denotes the I/O complexity of sorting N items. (Throughout this paper we assume that the dimension d is fixed). We also show how to dynamically maintain the WSPD in O log...

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Optimal Parallel All-Nearest-Neighbors Using the Well-Separated Pair Decomposition

W e present an optimal parallel algorithm t o construct the well-separated pair decomposition of a point set P in Zd. W e show how this leads to a deterministic opt imal O(1ogn) t ime parallel algorithm for finding the k nearest neighbors of each point in P, where k is a constant. W e discuss several additional applications of the well-separated pair decomposition for which we can derive fas t ...

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Bibliography of Literature

[3] P. B. Callahan, " Optimal parallel all-nearest-neighbors using the well-separated pair decomposition, " in

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تاریخ انتشار 2005