Before revision:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , 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 a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
After revision:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , 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 a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the geometric traveling salesman problem (path or tour version).