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 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).
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 geometric traveling salesman problem (path or tour version).
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and k nonredundant cuts
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k is a parameter dependent on P, a
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GTSP
geometric traveling salesman problem