We prove the following graph coloring result Let G be a connected bipartite planar graph Then one can triangulate G in such a way that the resulting graph is colorable This result implies several new upper bounds for guarding problems including the rst non trivial upper bound for the rectilinear Prison Yard Problem n vertex guards are su cient to watch the interior of a rectilinear polygon with...

We represent state machines in the category of speci cations, where assignment statements correspond exactly to interpretations between theories [7, 8]. However, the guards on an assignment require a special construction. In this paper we raise guards to the same level as assignments by treating each as a distinct category over a shared set of objects. A guarded assignment is represented as a p...

In this paper, we use an efficient art gallery-based algorithm for placing a small number of guards to inspect a 2D environment. The gallery models a 2D workspace for an autonomous robot. The proposed algorithm efficiently computes a near-optimal (small) number of guards in O(n log n) time and requires a linear storage complexity. An additional set of connection nodes are computed to form the c...

We propose a unified framework to study the walk problem in a polygonal area by two collaborative guards. A walk is conducted by the two mobile guards on the area’s boundary. They start at an initial boundary point, move along the boundary, and may possibly meet together again at an ending boundary point. It is required that the two guards maintain their mutual visibility at all times. Dependin...

In this paper, we consider the problem of placing a small number of angle guards inside a simple polygon P such that each point in the plane can determine if it is in or out of P from a monotone Boolean formula (and (.) and or (+) operations only) composed from the angle guards. Each angle guard views an infinite wedge of the plane. This class of new art gallery type problems is called sculptur...

A hidden guard set G is a set of point guards in polygon P that all points of the polygon are visible from some guards in G under the constraint that no two guards may see each other. In this paper, we consider the problem for finding minimum hidden guard sets in histogram polygons under orthogonal visibility. Two points p and q are orthogonally visible if the orthogonal bounding rectangle for ...

ACCORDING to the standard story, which is unfortunately still found in many physics textbooks, quantum theory emerged when it was realized that classical physics predicts an energy distribution for black-body radiation that disagrees violently with that found experimentally. In the late 1890s, so the story continues, the German physicist Wilhelm Wien developed an expression that corresponded re...