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: 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 at any place on the input curve, provided that they respect the order along the input curve.