A RANDOMIZED ALGORITHM FOR SLOPE SELECTION

Abstract

A set of n distinct points in the plane defines [Formula: see text] lines by joining each pair of distinct points. The median slope of these O(n 2 ) 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.