3 research outputs found
Discrete Surveillance Tours in Polygonal Domains
The watchman route of a polygon is a closed tour thatsees all points of the polygon. Computing the shortestsuch tour is a well-studied problem. Another reasonableoptimization criterion is to require that the tour mini-mizes the hiding time of the points in the polygon, i.e.,the maximum time during which any points is not seenby the agent following the tour at unit speed. We callsuch tours surveillance routes.We show a linear time 3/2-approximation algorithmfor the optimum surveillance tour problem in rectilin-ear polygons using the L_1 -metric. We also present apolynomial time O(polylog w_max )-approximation algo-rithm for the optimum weighted discrete surveillanceroute in a simple polygon with weight values in therange [1, w_max]
Discrete Surveillance Tours in Polygonal Domains
The watchman route of a polygon is a closed tour thatsees all points of the polygon. Computing the shortestsuch tour is a well-studied problem. Another reasonableoptimization criterion is to require that the tour mini-mizes the hiding time of the points in the polygon, i.e.,the maximum time during which any points is not seenby the agent following the tour at unit speed. We callsuch tours surveillance routes.We show a linear time 3/2-approximation algorithmfor the optimum surveillance tour problem in rectilin-ear polygons using the L_1 -metric. We also present apolynomial time O(polylog w_max )-approximation algo-rithm for the optimum weighted discrete surveillanceroute in a simple polygon with weight values in therange [1, w_max]
Discrete Surveillance Tours in Polygonal Domains
The watchman route of a polygon is a closed tour that
sees all points of the polygon. Computing the shortest
such tour is a well-studied problem. Another reasonable
optimization criterion is to require that the tour mini-
mizes the hiding time of the points in the polygon, i.e.,
the maximum time during which any points is not seen
by the agent following the tour at unit speed. We call
such tours surveillance routes.
We show a linear time 3/2-approximation algorithm
for the optimum surveillance tour problem in rectilin-
ear polygons using the L_1 -metric. We also present a
polynomial time O(polylog w_max )-approximation algo-
rithm for the optimum weighted discrete surveillance
route in a simple polygon with weight values in the
range [1, w_max]