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

Abstract

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 m2+⌊k4⌋+4 vertex guards are always sufficient. When the orthogonal polygons are arbitrary oriented, we show that m2+k+1 vertex guards are sometimes necessary and conjecture the bound is tight.