Geodesic
Visibility Graphs of Anchor Polygons
Journal of Graph Algorithms and Applications, Tome 26 (2022) no. 1, pp. 15-34.

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The visibility graph of a polygon corresponds to its internal diagonals and boundary edges. For each vertex on the boundary of the polygon, we have a vertex in this graph and if two vertices of the polygon see each other there is an edge between their corresponding vertices in the graph. Two vertices of a polygon see each other if and only if their connecting line segment completely lies inside the polygon. Recognizing visibility graphs is the problem of deciding whether there is a simple polygon whose visibility graph is isomorphic to a given graph. Another important problem is to reconstruct such a polygon if there is any. These problems are well known and well-studied, but yet open problems in geometric graphs and computational geometry. However, they have been solved efficiently for special cases where the target polygon is known to be a tower or a spiral polygon. In this paper, we propose a linear time algorithm to solve these recognizing and reconstruction problems for another type of polygons, named anchor polygons.
DOI : 10.7155/jgaa.00579
Keywords: anchor polygon‎, visibility graph, polygon reconstruction, recognizing visibility graph 
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Hossein Boomari; Alireza Zarei. Visibility Graphs of Anchor Polygons. Journal of Graph Algorithms and Applications, Tome 26 (2022) no. 1, pp. 15-34. doi : 10.7155/jgaa.00579. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00579/

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