Related papers: Pseudo-Triangle Visibility Graph: Characterization…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
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…
A shape visibility representation displays a graph so that each vertex is represented by an orthogonal polygon of a particular shape and for each edge there is a horizontal or vertical line of sight between the polygons assigned to its…
A transparent rectangle visibility graph (TRVG) is a graph whose vertices can be represented by a collection of non-overlapping rectangles in the plane whose sides are parallel to the axes such that two vertices are adjacent if and only if…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…
We study terrain visibility graphs, a well-known graph class closely related to polygon visibility graphs in computational geometry, for which a precise graph-theoretical characterization is still unknown. Over the last decade, terrain…
A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs…
Intersection graphs of geometric objects have been extensively studied, both due to their interesting structure and their numerous applications; prominent examples include interval graphs and permutation graphs. In this paper we study a…
We devise an algorithm for maintaining the visibility polygon of any query point in a dynamic polygonal domain, i.e., as the polygonal domain is modified with vertex insertions and deletions to its obstacles, we update the data structures…
An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations…
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P. We build a data structure in O(n) time and O(n) space that can compute the…
Any graph which is not vertex transitive has a proper induced subgraph which is unique due to its structure or the way of its connection to the rest of the graph. We have called such subgraph as an anchor. Using an anchor which, in fact, is…
Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the…
We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider a triangulated terrain with $m>1$ viewpoints (or guards) located on the terrain surface. A point on the terrain is considered…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
In this brief paper, a simple and fast computational method, the Planar Visibility Graph Networks Algorithm was proposed based on the famous Visibility Graph Algorithm, which can fulfill converting two dimensional timeseries into a planar…
We study unit disk visibility graphs, where the visibility relation between a pair of geometric entities is defined by not only obstacles, but also the distance between them. That is, two entities are not mutually visible if they are too…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…