  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 $O(kn^2)$ runtime that produces polygonal visibility paths (or
tours) of link-length at most $(\gamma+a_l/(k-1))Opt$ (or $(\gamma+a_l/k)Opt$),
where $k$ is a parameter dependent on $P$, $a_l$ is an output sensitive
parameter and $\gamma$ is the approximation factor of an $O(k^3)$ time
approximation algorithm for the graphic traveling salesman problem (path or
tour version).
