Convex Cover and Hidden Set in Funnel Polygons

Abstract

We present linear-time algorithms for both maximum hidden set and minimum convex cover in funnel polygons. These algorithms show that funnel polygons are "homestead" polygons, i.e. polygons for which the hidden set number and the convex cover number coincide. We extend the algorithm to apply to maximum hidden vertex set and use the result to give a 2-approximation for all three problems in pseudotriangles.