A randomized algorithm for slope selection

Michael B Dillencourt, David M. Mount, Nathan S. Netanyahu

Research output: Contribution to journalArticlepeer-review


A set of n distinct points in the plane defines lines by joining each pair of distinct points. The median slope of these O(n2) lines was proposed by Theil as a robust estimator for the slope of the line of best fit for the points. We present a randomized algorithm for selecting the k-th smallest slope of such a set of lines which runs in expected O(n log n) time. An efficient implementation of the algorithm and practical experience with the algorithm are discussed.
Original languageAmerican English
Pages (from-to)1-27
JournalInternational Journal of Computational Geometry and Applications
Issue number01
StatePublished - 1992


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