A Randomized Algorithm for Slope Selection

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

A Randomized Algorithm for Slope Selection

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

Department of Computer Science and Artificial Intelligence

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	American English
Title of host publication	Third Canadian Conference on Computational Geometry
State	Published - 1991

Bibliographical note

Place of conference:Vancouver, Canada

Cite this

@inproceedings{45a9f6665a2644708e410d72410d3750,

title = "A Randomized Algorithm for Slope Selection",

abstract = "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.",

author = "Dillencourt, \{Michael B.\} and Mount, \{David M.\} and Netanyahu, \{Nathan S.\}",

note = "Place of conference:Vancouver, Canada",

year = "1991",

language = "American English",

booktitle = "Third Canadian Conference on Computational Geometry",

}

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T1 - A Randomized Algorithm for Slope Selection

AU - Dillencourt, Michael B.

AU - Mount, David M.

AU - Netanyahu, Nathan S.

N1 - Place of conference:Vancouver, Canada

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

M3 - Conference contribution

BT - Third Canadian Conference on Computational Geometry

ER -

A Randomized Algorithm for Slope Selection

Abstract

Bibliographical note

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