Ortho-unit polygons can be guarded with at most $\lfloor \frac{n-4}{8}\rfloor$ guards

Abstract

An orthogonal polygon is called an ortho-unit polygon if its vertices have integer coordinates, and all of its edges have length one. In this paper we prove that any ortho-unit polygon with $n\ge 12$ vertices can be guarded with at most $\lfloor \frac{n-4}{8}\rfloor$ guards, which is a tight bound.

15 pages, 11 figures