Consider a rectangular art gallery divided into n rectangular rooms, such that any two rooms sharing a wall in common have a door connecting them. How many guards need to be stationed in the gallery so as to protect all of the rooms in our gallery? Notice that if a guard is stationed at a door, he will be able to guard two rooms. Our main aim in this paper is to show that Èn/2 ̆ guards are alway...

A polygon is called k-guardable if it is possible to find a collection G of points in the interior of the edges of P such that every point in P is visible from at least k elements of G, and such that no edge of P contains more than one element of G. In this paper we prove that every simple polygon can be 1-guarded using at most n/2 guards, and that every polygon with 0 or 1 polygonal hole can...

We devise an algorithm for surveying a dynamic orthogonal polygonal domain by placing one guard at each vertex in subset of its vertices, i.e., whenever [Formula: see text] is modified to result another text], our updates the set guards so that updated surveys text]. Our modifies placement amortized time, while ensuring with holes and vertices guarded using most guards. For special case initial...