Proceedings of the Annual Symposium on Computational Geometry
We extend the notion of polygon visibility graphs to pseudo-polygons defined on generalized configurations of points. We consider both vertex-to-vertex, as well as vertex-to-edge visibility in pseudo-polygons. We study the characterization and recognition problems for vertex-edge pseudo-visibility graphs. Given a bipartite graph G satisfying three simple properties, which can all be checked in polynomial time, we show that we can define a generalized configuration of points and a pseudo-polygon on it, so that its vertex-edge pseudo-visibility graph is G. This provides a full characterization of vertex-edge pseudo-visibility graphs and a polynomial-time algorithm for the decision problem. It also implies that the decision problem for vertex visibility graphs of pseudo-polygons is in NP (as opposed to the same problem with straight-edge visibility, which is only known to be in PSPACE).
© 1997 ACM
O'Rourke, Joseph and Streinu, Ileana, "Vertex-Edge Pseudo-Visibility Graphs: Characterization and Recognition" (1997). Computer Science: Faculty Publications, Smith College, Northampton, MA.