On determining the on-line minimax linear fit to a discrete point set in the plane

Abstract

An on-line algorithm for obtaining the minimax linear fit to a planar discrete set of points is presented. The algorithm depends on a new property of the convex hull. This property deals with the maximum vertical distance between a hull edge and the vertices of the hull. It states that, for consecutive bottom hull edges, this maximum vertical distance monotonically decreases to a minimum and then monotonically increases. An analogous property applies for the top hull.