An efficient randomized algorithm for the closest pair problem on colored point sets

  • Authors:
  • V. Kamakoti;Kamala Krithivasan;C. Pandu Rangan

  • Affiliations:
  • Department of Computer Science and Engineering, Indian Institute of Technology, Madras - 600 036 Tamilnadu, INDIA;Department of Computer Science and Engineering, Indian Institute of Technology, Madras - 600 036 Tamilnadu, INDIA;Department of Computer Science and Engineering, Indian Institute of Technology, Madras - 600 036 Tamilnadu, INDIA

  • Venue:
  • Nordic Journal of Computing
  • Year:
  • 1995

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Abstract

We present a simple randomized algorithm for finding the Closest Foreign Pair, in a set of n points in D-dimensional space, where D ≥ 2 is a fixed constant and the distances are measured in the L1 and the L∞ metric. The algorithm runs in O(nlogD-1 n/log log n) time with high probability for the L∞ metric and in O(n log2D-1-1 n/log log n) time with high probability for the L1 metric.