Summary: Polyline Fitting of Planar Points under Min-Sum Criteria
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 min-sum criteria with respect to L1- and L2-metrics, which are more appropriate measures
than uniform and Hausdorff metrics in statistical context. We present efficient algorithms for
the 1-joint versions of the problem and fully polynomial-time approximation schemes for the
general k-joint versions.
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
non-linear regression approximates it by a non-linear 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