Approximate Curve-Restricted Simplification of Polygonal Curves

The goal in the min-\# curve simplification problem is to reduce the number of the vertices of a polygonal curve without changing its shape significantly. We study curve-restricted min-\# simplification of polygonal curves, in which the vertices of the simplified curve can be placed on any point of the input curve, provided that they respect the order along that curve. For local directed Hausdorff distance from the input to the simplified curve in $\mathbb{R}^2$, we present an approximation algorithm that computes a curve whose number of links is at most twice the minimum possible.