We study the problem of colouring the vertices of a polygon, such that every viewer can see
a unique colour. The goal is to minimize the number of colours used. This is also known as …

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 …

Let P be an orthogonal polygon. Consider a sliding camera that travels back and forth along
an orthogonal line segment s⊆ P as its trajectory. The camera can see a point p∈ P if there …

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 …

A sliding camera in an orthogonal polygon P—that is, a polygon all of whose edges are axis-
parallel—is a point guard g that travels back and forth along an axis-parallel line segment s …

Let P be an orthogonal polygon with n vertices. A partition of P into rectangles is called
conforming if it results from cutting P along a set of interior-disjoint line segments, each …

There exist many variants of guarding an orthogonal polygon in an orthogonal fashion:
sometimes a guard can see within a rectangle, along a staircase, or along an orthogonal …

The stabbing number of a partition of a rectilinear polygon P into rectangles is the maximum
number of rectangles stabbed by any axis-parallel line segment contained in P. We consider …

The art gallery problem or museum problem is a wellknown visibility problem in
computational geometry. It originates from a real-world problem of guarding an art gallery …

In this paper, we consider a new variant of covering in an orthogonal art gallery problem
where each guard is a sliding k-transmitter. Such a guard can travel back and forth along an …