Art Gallery Problem with Rook and Queen Vision

A chromatic art gallery problem

The art gallery problem asks for the smallest number of guards required to see every point of the interior of a polygon P . We introduce and study a similar problem called the chromatic art gallery problem. Suppose that two members of a finite point guard set S ⊂ P must be given different colors if their visible regions overlap. What is the minimum number of colors required to color any guard s...

Two-Guard Art Gallery Problem

Coloring Variations of the Art Gallery Problem

The art gallery problem [2] asks for the smallest possible size of a point set S (the guards) to completely guard the interior of a simple polygon P (the art gallery). This thesis treats variations of the original problem that arise when we introduce a coloring of the guards. Rather than asking for the minimum number of guards we ask for the minimum number of colors. In [4] L. H. Erickson and S...

On the Chromatic Art Gallery Problem

For a polygonal region P with n vertices, a guard cover S is a set of points in P , such that any point in P can be seen from a point in S. In a colored guard cover, every element in a guard cover is assigned a color, such that no two guards with the same color have overlapping visibility regions. The Chromatic Art Gallery Problem (CAGP) asks for the minimum number of colors for which a colored...

An Approximation Algorithm for the Art Gallery Problem

Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The point-guard art gallery problem asks for a minimum set S such that every point in P is visible from a point in S. Assuming integer coordinates and a special general position assumption, we present the first O(log OPT)-approximation algorith...