Dice Question Streamline Icon: https://streamlinehq.com

Recognition of Simple Polygon Visibility Graphs

Determine the computational complexity of recognizing visibility graphs of simple polygons, including the variant in which the cyclic order of vertices along the polygon boundary is given.

Information Square Streamline Icon: https://streamlinehq.com

Background

Visibility graphs record which pairs of polygon vertices are mutually visible within the polygon, a classical structure in computational geometry with many applications.

While recognition is ER-complete for polygons with holes, the simple polygon case—and the case with prescribed boundary ordering—remains unresolved.

References

Still, the computational complexity of the recognition problem for simple polygon visibility graphs remains open, even for the variant in which the ordering of the vertices along the polygon is given.

— The Existential Theory of the Reals as a Complexity Class: A Compendium (2407.18006 - Schaefer et al., 25 Jul 2024) in Section “Visibility Graphs”