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A simple approximation algorithm for the diameter of a set of points in an Euclidean plane

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  • Jieying Hong
  • Zhipeng Wang
  • Wei Niu

Abstract

Approximation algorithms with linear complexities are required in the treatments of big data, however, present algorithms cannot output the diameter of a set of points with arbitrary accuracy and near-linear complexity. By introducing the partition technique, we introduce a very simple approximation algorithm with arbitrary accuracy ε and a complexity of O(N + ε−1 log ε−1) for the cases that all points are located in an Euclidean plane. The error bounds are proved strictly, and are verified by numerical tests. This complexity is better than existing algorithms, and the present algorithm is also very simple to be implemented in applications.

Suggested Citation

  • Jieying Hong & Zhipeng Wang & Wei Niu, 2019. "A simple approximation algorithm for the diameter of a set of points in an Euclidean plane," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-13, February.
    • Handle: RePEc:plo:pone00:0211201
    DOI: 10.1371/journal.pone.0211201
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