Before revision: In this paper we study curve-restricted min-\# simplification of polygonal curves, in which the vertices of the simplified curve can be placed at any place on the input curve, provided that they respect the order along the input curve.
After revision: In this paper 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 the input curve.