Distinct distances determined by subsets of a point set in space

David Avis, Paul Erdős, János Pach

Research output: Contribution to journalArticle

10 Citations (Scopus)


We answer the following question posed by Paul Erdős and George Purdy: determine the largest number f d (k) = f with the property that almost all k-element subsets of any n-element set in R d determine at least f distinct distances, for all sufficiently large n. For d = 2 we investigate the asymptotic behaviour of the maximum number of k-element subsets of a set of n points, each subset determining at most i distinct distances, for some prespecified number i. We also show that if k = o(n 1 7 ), almost all k-element subsets of a planar point set determine distinct distances.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalComputational Geometry: Theory and Applications
Issue number1
Publication statusPublished - Jul 1991


ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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