A simple scalable linear time algorithm for horizontal visibility graphs

Schmidt, Jonas; Köhne, Daniel

doi:10.1016/j.physa.2023.128601

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2024

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“…Using the O(n) time triangulation algorithm of Chazelle [4] reduces the running-time of Hershberger's result to O(m + n) which is optimal. There are numerous recent results considering properties of the visibility graph [5,6], visibility graphs of special polygons [7] and visibility graph applications [8].…”

Section: Introductionmentioning

confidence: 99%

Pseudo-Triangle Visibility Graph: Characterization and Reconstruction

Mehrpour,

Zarei

2024

Scientia Iranica

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The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices in a plane such that it will be consistent with this visibility graph. This problem has been solved for special cases when we know that the target is a tower, a spiral, or an anchor polygon. Knowing that a given visibility graph belongs to a simple polygon with at most three concave chains on its boundary, a pseudo-triangle, we propose a linear-time algorithm for reconstructing one of its corresponding polygons. Moreover, we introduce a set of necessary and sufficient properties for characterizing visibility graphs of pseudo-triangles and propose polynomial algorithms for checking these properties.

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