Open Guard Edges and Edge Guards in Simple Polygons [chapter]

Csaba D. Tóth, Godfried T. Toussaint, Andrew Winslow
2012 Lecture Notes in Computer Science  
An open edge of a simple polygon is the set of points in the relative interior of an edge. We revisit several art gallery problems, previously considered for closed edge guards, using open edge guards. A guard edge of a polygon is an edge that sees every point inside the polygon. We show that every simple non-starshaped polygon admits at most one open guard edge, and give a simple new proof that it admits at most three closed guard edges. We characterize open guard edges, and derive an
more » ... that finds all open guard edges of a simple n-gon in O(n) time in the RAM model of computation. Finally, we present lower bound constructions for simple polygons with n vertices that require n/3 open edge guards, and conjecture that this bound is tight.
doi:10.1007/978-3-642-34191-5_5 fatcat:jiw37p64hnah5i6duxmi77all4