Recognition and Reconstruction of Visibility Gragh in Special Cases

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Yazdani Ghooshchi, Mina | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52414 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireza
Abstract:
For a simple polygon in the plane, the visibility graph is a graph whose vertices are the vertices of the polygon and there is an edge between two vertices if and only if their corresponding vertices see each other in the polygon. Two points of the polygon see each other if the line segment connecting them lies completely inside (or on the boundary of) the polygon. Although computing the visibility graph of a polygon has been solved efficiently, its reverse problem after three decades is still an open problem. The reverse problem is known as recognition and reconstruction visibility graphs. Recognizing visibility graphs is to determine the necessary and sufficient conditions on a graph to be a visibility graph of a polygon in the plane and in its reconstruction is to provide such a polygon whose visibility graph is isomorphic to the given visibility graph. In this thesis, we survey the current results for this problem and purpose a method for solving this problem in some special cases
Keywords:
Computational Geometry ; Visibility Graph ; Reconstruction ; Visibility Graph Recognition