William L. Steiger

An optimal-time algorithm for slope selection

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

Least Absolute Deviations Curve-Fitting

O(n)

Algorithms for ham-sandwich cuts

, line sweeping gives an optimal,

Algorithms and complexity for least median of squares regression

O(n\log n)

An upper bound on the number of planarK-sets

-time algorithm. For general k the parametric search technique of Megiddo is used to describe an

Geometric medians

O(n(\log n)^2 )

Optimization in Arrangements

-time algorithm. This is modified to produce a new, optimal

Optimal parallel selection had complexity O (log log N )

O(n\log n)

On a matching problem in the plane

-time selection algorithm by incorporating an approximation idea.

The parallel complexity of element distinctness is Ω(√log n)

A method is proposed for least absolute deviations curve fitting. It may be used to obtain least absolute deviations fits of general linear regressions. As a special case it includes a minor variant of a method for fitting straight lines by least absolute deviations that was previously thought to possess no generalization. The method has been tested on a computer and was found on a range of problems to execute in as little as