 
Summary: Polyline Fitting of Planar Points under MinSum Criteria
Boris Aronov
Tetsuo Asano
Naoki Katoh
Kurt Mehlhorn§
Takeshi Tokuyama¶
Abstract
Fitting a curve of a certain type to a given set of points in the plane is a basic problem in
statistics and has numerous applications. We consider fitting a polyline with k joints under
the minsum criteria with respect to L1 and L2metrics, which are more appropriate measures
than uniform and Hausdorff metrics in statistical context. We present efficient algorithms for
the 1joint versions of the problem and fully polynomialtime approximation schemes for the
general kjoint versions.
1 Introduction
Curve fitting aims to approximate a given set of points in the plane by a curve of a certain type.
This is a fundamental problem in statistics, and has numerous applications. In particular, it is a
basic operation in regression analysis. Linear regression approximates a point set by a line, while
nonlinear regression approximates it by a nonlinear function from a given family.
In this paper, we consider the case where the points are fitted by a polygonal curve (polyline)
with k joints, see Figure 1. This is often referred to as polygonal approximation or polygonal
