Optimal slope selection via expanders

Matthew J. Katz, Micha Sharir

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Given n points in the plane and an integer k, the slope selection problem is to find the pair of points whose connecting line has the kth smallest slope. (In dual setting, given n lines in the plane, we want to find the vertex of their arrangement with the kth smallest x-coordinate.) Cole et al. have given an O(n log n) solution (which is optimal), using the parametric searching technique of Megiddo. We obtain another optimal (deterministic) solution that does not depend on parametric searching and uses expander graphs instead. Our solution is somewhat simpler than that of [6] and has a more explicit geometric interpretation.

Original languageEnglish
Pages (from-to)115-122
Number of pages8
JournalInformation Processing Letters
Issue number3
StatePublished - 14 Sep 1993
Externally publishedYes


  • Computational geometry
  • algorithms
  • design of algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


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