Finding the Hamiltonian Cycle Corresponding to the Boundary of a Pseudo-Triangle in its Visibility Graph

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Farokhi, Soheila | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50786 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireza
Abstract:
The visibility graph of a simple polygon represents visibility relations between its vertices. Since each vertex in a polygon is visible from the two vertices adjacent to it on the boundary of the polygon, this boundary is analogous to a Hamiltonian cycle in the visibility graph of the polygon. Therefore, visibility graphs are Hamiltonian. Finding this Hamiltonian cycle can be of great help when solving visibility graph recognition problems, in which one should decide whether a given graph is a visibility graph of a simple polygon; and reconstruction problems, which include constructing the polygon corresponding to a given visibility graph. These problems have been solved for the special cases of spiral and tower polygons. In this study, we introduce a polynomial algorithm to find the Hamiltonian cycle corresponding to the boundary of a polygon with three concave chains on its boundary, called a pseudo-triangle, in its visibility graph
Keywords:
Visibility Graph ; Computational Geometry ; Hamiltonian Cycle Problem ; Pseudo-Triangle