New bounds on guarding problems for orthogonal polygons in the plane using vertex guards with halfplane vision.

• Guarding disjoint monotone orthogonal polygons in a plane. • Guarding a rectangular polygon with orthogonal holes. • Rectilinear Art Gallery Problem. • Guards with restricted visibility. Given a set F of k disjoint monotone orthogonal polygons with a total of m vertices, we present bounds on the number of vertex guards required to guard the free space and the boundaries of the polygons in F when the range of vision of each guard is bounded by 180∘ (the region in front of the guard). When the orthogonal polygons are axis aligned we prove that m 2 + ⌊ k 4 ⌋ + 4 vertex guards are always sufficient. When the orthogonal polygons are arbitrary oriented, we show that m 2 + k + 1 vertex guards are sometimes necessary and conjecture the bound is tight. [ABSTRACT FROM AUTHOR]