
Recognizing Visibility Graphs of Polygons with Holes and InternalExternal Visibility Graphs of Polygons
Visibility graph of a polygon corresponds to its internal diagonals and ...
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Computational Complexity Aspects of Point Visibility Graphs
A point visibility graph is a graph induced by a set of points in the pl...
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Computing Boundary Cycle of a PseudoTriangle Polygon from its Visibility Graph
Visibility graph of a simple polygon is a graph with the same vertex set...
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PseudoTriangle Visibility Graph: Characterization and Reconstruction
The visibility graph of a simple polygon represents visibility relations...
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BoundedDegree Spanners in the Presence of Polygonal Obstacles
Let V be a finite set of vertices in the plane and S be a finite set of ...
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Shortest Watchman Tours in Simple Polygons under Rotated Monotone Visibility
We present an O(nrG) time algorithm for computing and maintaining a mini...
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Combinatorial Properties and Recognition of Unit Square Visibility Graphs
Unit square (grid) visibility graphs (USV and USGV, resp.) are described...
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Recognizing Visibility Graphs of Triangulated Irregular Networks
A Triangulated Irregular Network (TIN) is a data structure that is usually used for representing and storing monotone geographic surfaces, approximately. In this representation, the surface is approximated by a set of triangular faces whose projection on the XYplane is a triangulation. The visibility graph of a TIN is a graph whose vertices correspond to the vertices of the TIN and there is an edge between two vertices if their corresponding vertices on TIN see each other, i.e. the segment that connects these vertices completely lies above the TIN. Computing the visibility graph of a TIN and its properties have been considered thoroughly in the literature. In this paper, we consider this problem in reverse: Given a graph G, is there a TIN with the same visibility graph as G? We show that this problem is Complete for Existential Theory of The Reals.
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