mobile guard

Art Gallery Problems

Mobile vs. point guards

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover the gallery …

Mobile vs. point guards in orthogonal art gallery theorems

Our results are concerned with art gallery theorems on orthogonal polygons. We prove that an n-vertex orthogonal polygon can be partitioned into $\lfloor\frac{3n+4}{16}\rfloor$ at most 8-vertex pieces. This directly implies Aggarwal's theorem, namely …

Partitioning orthogonal polygons into at most 8-vertex pieces, with application to an art gallery theorem

We prove that every simply connected orthogonal polygon of $n$ vertices can be partitioned into $\lfloor\frac{3n+4}{16}\rfloor$ (simply connected) orthogonal polygons of at most 8 vertices. It yields a new and shorter proof of the theorem of A. …