Reprint of: Upward planar embedding of an n -vertex oriented path on O(n2)O(n2) points

We prove that every n  -vertex oriented path admits an upward planar embedding on every general set of (n−1)2+1(n−1)2+1 points on the plane. This result improves the previously known upper bound which is exponential in the number of switches of the given oriented path (Angelini et al. 2010) [1].