An Algorithm for Visibility Graph Recognition on Planar Graphs

Abstract

To decide whether a given graph is the visibility graph of some simple polygon, is not known to be NP, nor is it known to be NP-hard. It is only known to be PSPACE. The problem of characterizing visibility graphs of an arbitrary simple polygons and the related problem of efficiently recognizing such graphs have remained important open problem in computational geometry. In this paper, an algorithm for visibility graph recognition on embedded planar graphs is presented. Proposed algorithm gets a embedded planar graph and recognizes whether it is a visibility graph. Time complexity of the algorithm is polynomial.