… method, one can obtain a PTAS for optimally guarding polyominoes with guards of limited
visibility [16]. We focus here on pixel guards within thin polyomino trees. In this case we have …

… to guard an m-polyomino. We consider both point guards and pixel guards. We show that
determining the pixel guard number for a given m-polyomino is NP-hard. We give a simple …

… An m-polyomino is the connected union of m unit squares called … guarding polyominoes
and polycubes and obtain simpler proofs. We also obtain new art gallery theorems for guarding …

… by the guards that see each viewpoint. For larger k, we keep the placement of guards, but the
polyomino will … Because of the relative position of the guards they are shattered as before. …

… cover any m-polyomino. In this paper we improve this bound, showing that an m-polyomino …
can assume that Pm is the union of an 11-polyomino P11 and an (m−11)-polyomino Pm−11. …

… We study the art gallery problem when the instance is a polyomino, which is … guards with
\(r\)-visibility in a polyomino with holes is NP-hard. Here, two points \(u\) and \(v\) on a polyomino …

… -polyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding
polyominoes in … In particular, we show that \(\lfloor\frac{m+1}{3} \rfloor\) point guards are …

… implies a solution to the instance of PLANAR 3SAT, thus establishing that guarding
polyominoes with holes under the r-visibility model is NP-hard. Alpert and Roldán [3] investigate a …

… Assume we are given a polygon P, a region U ⊆ P to be guarded, and a set Γ of guards
allowed to be used. In what follows, we treat any element γ ∈ Γ as a set, so either γ = ψ is a pixel…

… guarding a TOP is NP-hard for vertex or boundary guards. We remark that the proofs developed
previously for polyominoes [4… contains the class of thin polyomino trees introduced in [4], …