Optimal slope selection

  • Richard Cole
  • Jeffrey Salowe
  • W. L. Steiger
  • Endre Szemerédi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)


Given n points in the plane and an integer k, we consider the problem of selecting that pair which determines the line with the kth smallest or largest slope. In the restricted case where k is O(n), line sweeping gives an optimal, Θ(nlog n) algorithm. For general k we use the parametric search technique of Megiddo to describe an O(n (log n)2) algorithm. This is modified to produce a new, optimal Θ(nlog n) selection algorithm by incorporating an approximation idea.


Linear Time Query Point Delete Line Sorting Network Approximate Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Richard Cole
    • 1
  • Jeffrey Salowe
    • 2
  • W. L. Steiger
    • 3
  • Endre Szemerédi
    • 4
    • 5
  1. 1.Courant InstituteNew York UniversityNew York
  2. 2.Computer ScienceUniversity of VirginiaCharlottesville
  3. 3.Computer ScienceRutgers UniversityNew Brunswick
  4. 4.Computer ScienceRutgers UniversityUSA
  5. 5.Mathematical InstituteHungarian Academy of SciencesHungary

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