Watchman route in a simple polygon with a rubberband algorithm

So far, the best result in running time for solving the fixed watchman route problem (i.e., shortest path for viewing any point in a simple polygon with given start point) is O(n 3 log n), published in 2003 by M. Dror, A. Efrat, A. Lubiw, and J. Mitchell. -This paper provides an algorithm with κ(ε) · O(kn) runtime, where n is the number of vertices of the given simple polygon Π, and k the number of essential cuts; κ(ε) defines the numerical accuracy in dependency of a selected constant ε > 0. Moreover, our algorithm is significantly simpler, easier to understand and implement than previous ones for solving the fixed watchman route problem