  How many chess rooks or queens does it take to guard all the squares of a
given polyomino, the union of square tiles from a square grid? This question is
a version of the art gallery problem in which the guards can "see" whichever
squares the rook or queen attacks. We show that floor(n/2) rooks or floor(n/3)
queens are sufficient and sometimes necessary to guard a polyomino with n
tiles. We also prove that finding the minimum number of rooks or the minimum
number of queens needed to guard a polyomino is NP-hard. These results also
apply to d-dimensional rooks and queens on d-dimensional polycubes. We also use
bipartite matching theorems to describe sets of non-attacking rooks on
polyominoes.
