This paper examines differences of four approaches in finding the visibility graph of a polygonal region with obstacles defined by simple polygons. Each has been implemented and tuned. Experimental comparisons via time measurements have been carried out against a variety of testcases ranging in graph density from maximal, O(† n 2), to minimal, † W(n). In this manner, expected asymptotic time bo...

We characterize two types of bar-visibility graphs on the Mobius band (abbreviated "BVGMs"), in which vertices correspond to intervals that are parallel or orthogonal to the axis of the band, depen­ ding on type, and in which adjacency corresponds to orthogonal visibility of intervals. BVGMs with intervals orthogonal to the axis are shown to be equivalent to the "polar visibility graphs" studie...

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of visibility graph motifs, smaller substructures that appear with characteristic frequencies. We develop ...

In this paper, we give a characterization of the visibility graphs of pseudo-polygons. We first identify some key combinatorial properties of pseudo-polygons, and we then give a set of five necessary conditions based off our identified properties. We then prove that these necessary conditions are also sufficient via a reduction to a characterization of vertex-edge visibility graphs given by O’R...

A visibility representation of a graph maps vertices to horizontal segments and edges to vertical segments. For a weak-visibility representation, if the vertices of the original graph are adjacent, the corresponding segments will ’see’ each other. For a strong-visibility representation, the converse is true as well. Here we present a detailed step-by-step construction of a weak-visibility repre...

Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axisparallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i. e., the problem of representing USGV with fixed visibilities within small area and, for USV, the gener...