New Bounds On Guarding Problems For Orthogonal Polygons In The Plane Using Vertex Guards With Halfplane Vision

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 degrees (the region in front of the guard). When the orthogonal polygons are axis aligned we prove that m/2 + left perpendiculark/4right perpendicular + 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. (C) 2021 Elsevier B.V. All rights reserved.