Abstract
Visibility graph of a simple polygon is a graph with the same vertex set in which there is an edge between a pair of vertices if and only if the segment through them lies completely inside the polygon. Each pair of adjacent vertices on the boundary of the polygon are assumed to be visible. Therefore, the visibility graph of each polygon always contains its boundary edges. This implies that we have always a Hamiltonian cycle in a visibility graph which determines the order of vertices on the boundary of the corresponding polygon. In this paper, we propose a polynomial time algorithm for determining such a Hamiltonian cycle for a pseudo-triangle polygon from its visibility graph.
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References
Belta, C., Isler, V., Pappas, G.J.: Discrete abstractions for robot motion planning and control in polygonal environments. IEEE Trans. Robot. 21(5), 864–874 (2005)
Colley, P., Lubiw, A., Spinrad, J.: Visibility graphs of towers. Comput. Geom. 7(3), 161–172 (1997)
Everett, H.: Visibility graph recognition - P.hD. thesis (1990)
Everett, H., Corneil, D.G.: Recognizing visibility graphs of spiral polygons. J. Algorithms 11(1), 1–26 (1990)
Ghosh, S.K.: Visibility Algorithms in the Plane. Cambridge University Press, Cambridge (2007)
Mehrpour, S., Zarei, A.: Pseudo-triangle visibility graph: characterization and reconstruction (2019)
Richter-Gebert, J.: Mnëv’s universality theorem revisited. Séminaire Lotaringien de Combinatorie (1995)
Teller, S., Hanrahan, P.: Global visibility algorithms for illumination computations. In: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, pp. 239–246. ACM (1993)
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Boomari, H., Farokhi, S. (2020). Computing Boundary Cycle of a Pseudo-Triangle Polygon from Its Visibility Graph. In: S. Barbosa, L., Ali Abam, M. (eds) Topics in Theoretical Computer Science. TTCS 2020. Lecture Notes in Computer Science(), vol 12281. Springer, Cham. https://doi.org/10.1007/978-3-030-57852-7_5
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DOI: https://doi.org/10.1007/978-3-030-57852-7_5
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