The Complexity of Guarding Monotone Polygons

Altitude Terrain Guarding and Guarding Uni-Monotone Polygons

We show that the problem of guarding an x-monotone terrain from an altitude line and the problem of guarding a uni-monotone polygon are equivalent. We present a polynomial time algorithm for both problems, and show that the cardinality of a minimum guard set and the cardinality of a maximum witness set coincide. Thus, uni-monotone polygons are perfect; this result also extends to monotone mount...

Optimal guarding of polygons and monotone chains

In this paper we study several problems concerning the guarding of a polygon or a x-monotone polygonal chain P with n vertices from a set of points lying on it. Our results are: (1) An O(n logn) time sequential algorithm for computing the shortest guarding boundary chain of a polygon P. (2) An O(n logn) time sequential algorithm for computing the smallest set of consecutive edges guarding a pol...

Approximate Guarding of Monotone and Re tilinear Polygons

Guarding curvilinear art galleries with vertex or point guards

One of the earliest and most well known problems in computational geometry is the socalled art gallery problem. The goal is to compute the minimum possible number guards placed on the vertices of a simple polygon in such a way that they cover the interior of the polygon. In this paper we consider the problem of guarding an art gallery which is modeled as a polygon with curvilinear walls. Our ma...

Guarding Monotone Art Galleries with Sliding Cameras in Linear Time

A sliding camera in an orthogonal polygon P is a point guard g that travels back and forth along an orthogonal line segment s inside P . A point p in P is guarded by g if and only if there exists a point q on s such that line segment pq is normal to s and contained in P . In the minimum sliding cameras (MSC) problem, the objective is to guard P with the minimum number of sliding cameras. We giv...