Orthogonal art galleries with interior walls

Abstract

Consider an art gallery formed by a polygon on n vertices with m pairs of vertices joined by interior diagonals, the interior walls. Suppose that all walls (interior as well as exterior) are horizontal or vertical and each interior wall has an arbitrarily placed, arbitrarily small doorway. We show that the minimum number of guards that suffice to guard all such art galleries with n vertices and m interior walls is min { ⌊ ( n + 2 m ) / 4 ⌋ , ⌊ ( n + 3 ⌊ n / 2 ⌋ + m - 2 ) / 8 ⌋ } .