Optimal-time algorithm for slope selection

Richard Cole, Jeffrey S. Salowe, W. L. Steiger, Endre Szemeredi

Research output: Contribution to journalArticle

Abstract

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

Original languageEnglish (US)
Pages (from-to)792-810
Number of pages19
JournalSIAM Journal on Computing
Volume18
Issue number4
StatePublished - Aug 1989

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Slope
Parametric Search
Sweeping
Line
Integer
Approximation

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Cole, R., Salowe, J. S., Steiger, W. L., & Szemeredi, E. (1989). Optimal-time algorithm for slope selection. SIAM Journal on Computing, 18(4), 792-810.

Optimal-time algorithm for slope selection. / Cole, Richard; Salowe, Jeffrey S.; Steiger, W. L.; Szemeredi, Endre.

In: SIAM Journal on Computing, Vol. 18, No. 4, 08.1989, p. 792-810.

Research output: Contribution to journalArticle

Cole, R, Salowe, JS, Steiger, WL & Szemeredi, E 1989, 'Optimal-time algorithm for slope selection', SIAM Journal on Computing, vol. 18, no. 4, pp. 792-810.
Cole R, Salowe JS, Steiger WL, Szemeredi E. Optimal-time algorithm for slope selection. SIAM Journal on Computing. 1989 Aug;18(4):792-810.
Cole, Richard ; Salowe, Jeffrey S. ; Steiger, W. L. ; Szemeredi, Endre. / Optimal-time algorithm for slope selection. In: SIAM Journal on Computing. 1989 ; Vol. 18, No. 4. pp. 792-810.
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