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An optimal algorithm for the on-line closest-pair problem

Schwarz, Christian and Smid, Michiel and Snoeyink, Jack

MPI-I-91-123. November 1991, 11 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We give an algorithm that computes the closest pair in a set
of $n$ points in $k$-dimensional space on-line, in $O(n \log n)$
ime. The algorithm only uses algebraic functions and, therefore,
is optimal. The algorithm maintains a hierarchical subdivision of $k$-space
into hyperrectangles, which is stored in a binary
tree. Centroids are used to maintain a balanced decomposition
of this tree.
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  AUTHOR = {Schwarz, Christian and Smid, Michiel and Snoeyink, Jack},
  TITLE = {An optimal algorithm for the on-line closest-pair problem},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-91-123},
  MONTH = {November},
  YEAR = {1991},
  ISSN = {0946-011X},