On Guarding Orthogonal Polygons with Bounded Treewidth
نویسندگان
چکیده
There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see an entire rectangle, or along a staircase, or along a orthogonal path with at most k bends. In this paper, we study all these guarding models in the special case of orthogonal polygons that have bounded treewidth in some sense. Exploiting algorithms for graphs of bounded treewidth, we show that the problem of finding the minimum number of guards in these models becomes linear-time solvable in polygons of bounded treewidth.
منابع مشابه
On Guarding Orthogonal Polygons with Sliding Cameras
A sliding camera inside an orthogonal polygon P is a point guard that travels back and forth along an orthogonal line segment γ in P . The sliding camera g can see a point p in P if the perpendicular from p onto γ is inside P . In this paper, we give the first constant-factor approximation algorithm for the problem of guarding P with the minimum number of sliding cameras. Next, we show that the...
متن کاملGuarding Path Polygons with Orthogonal Visibility
We are interested in the problem of guarding simple orthogonal polygons with the minimum number of r-guards. The interior point p belongs an orthogonal polygon P is visible from r-guard g, if the minimum area rectangle contained p and q lies within P . A set of point guards in polygon P is named guard set (as denoted G) if the union of visibility areas of these point guards be equal to polygon ...
متن کاملNon-orthogonal ray guarding
In an earlier paper the notion of a ray guard, a guard that can only see along a single ray, was introduced. Ray guarding means siting the fewest possible guards that guard all adjacencies (shared edges or parts of edges) in an orthogonal arrangement of adjacent nonoverlapping rectangles. In the earlier paper the problem was restricted by requiring that the direction of sight be parallel to one...
متن کاملTight Bounds for Conflict-Free Chromatic Guarding of Orthogonal Art Galleries
The chromatic art gallery problem asks for the minimum number of “colors” t so that a collection of point guards, each assigned one of the t colors, can see the entire polygon subject to some conditions on the colors visible to each point. In this paper, we explore this problem for orthogonal polygons using orthogonal visibility—two points p and q are mutually visible if the smallest axisaligne...
متن کاملOn r-Guarding Thin Orthogonal Polygons
Guarding a polygon with few guards is an old and well-studied problem in computational geometry. Here we consider the following variant: We assume that the polygon is orthogonal and thin in some sense, and we consider a point p to guard a point q if and only if the minimum axis-aligned rectangle spanned by p and q is inside the polygon. A simple proof shows that this problem is NP-hard on ortho...
متن کامل