On Counting Monotone Polygons and Holes in a Point Set
Sang-Won Bae · Journal of Computing Science and Engineering · 2023
In this paper, we study the problem of counting the number of monotone polygons in a given set S of n points in general position in the plane. A simple polygon is said to be monotone when any vertical line intersects its boundary at most twice. To our best knowledge, this counting problem remains unsolved and no nontrivial algorithm is known so far. As a research step forward to tackle the problem, we define a subclass of monotone polygons and present the first efficient algorithms that exactly count them.