On approximations to minimum link visibility paths in simple polygons

We investigate a practical variant of the well-known polygonal visibility path (watchman) problem. For a polygon P, a minimum link visibility path is a polygonal visibility path in P that has the minimum number of links. The problem of finding a minimum link visibility path is NP-hard for simple polygons. If the link-length (number of links) of a minimum link visibility path (tour) is Opt for a simple polygon P with n vertices, we provide an algorithm with runtime that produces polygonal visibility paths (or tours) of link-length at most (or ), where k is a parameter dependent on P, is an output sensitive parameter and γ is the approximation factor of an time approximation algorithm for the geometric travelling salesman problem (path or tour version).