Efficient algorithms for computing the maximum distance between two finite planar sets

Binay K. Bhattacharya, Godfried T. Toussaint

Research output: Contribution to journalArticle


An 0(n log n) algorithm is presented for computing the maximum euclidean distance between two finite planar sets of n points. When the n points form the vertices of simple polygons this complexity can be reduced to 0(n). The algorithm is empirically compared to the brute-force method as well as an alternate 0(n2) algorithm. Both the 0(n log n) and 0(n2) algorithms run in 0(n) expected time for many underlying distributions of the points. An ε{lunate}-approximate algorithm can be obtained that runs in 0(n + 1 ε{lunate}) worst-case time.

Original languageEnglish (US)
Pages (from-to)121-136
Number of pages16
JournalJournal of Algorithms
Issue number2
StatePublished - Jun 1983


ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Computational Theory and Mathematics

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