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Related papers: Some Results On Point Visibility Graphs

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Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…

Computational Geometry · Computer Science 2014-03-18 Francisc Bungiu , Michael Hemmer , John Hershberger , Kan Huang , Alexander Kröller

A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertex-segments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices;…

Computational Geometry · Computer Science 2013-08-26 Franz J. Brandenburg

A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…

Computational Geometry · Computer Science 2019-09-04 Therese Biedl , Giuseppe Liotta , Fabrizio Montecchiani

This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing the concept of level of visibility, we are able to analyze…

Number Theory · Mathematics 2020-05-29 Kui Liu , Xianchang Meng

We study the problem of recovering the relative positions of objects moving along the real line based only on pairwise collision data. While interaction-based sensing systems arise naturally in a variety of practical settings, a systematic…

Discrete Mathematics · Computer Science 2026-05-25 Yun-Han Li , Ilan Shomorony , Olgica Milenkovic

We establish a one-to-one correspondence between 1-planar graphs and general and hole-free 4-map graphs and show that 1-planar graphs can be recognized in polynomial time if they are crossing-augmented, fully triangulated, and maximal…

Computational Geometry · Computer Science 2015-09-14 Franz J. Brandenburg

A graph $G$ is a $(\Pi_A,\Pi_B)$-graph if $V(G)$ can be bipartitioned into $A$ and $B$ such that $G[A]$ satisfies property $\Pi_A$ and $G[B]$ satisfies property $\Pi_B$. The $(\Pi_{A},\Pi_{B})$-Recognition problem is to recognize whether a…

Computational Complexity · Computer Science 2018-01-08 Iyad Kanj , Christian Komusiewicz , Manuel Sorge , Erik Jan van Leeuwen

In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to…

Data Structures and Algorithms · Computer Science 2017-07-24 Patrizio Angelini , Michael A. Bekos

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…

Data Analysis, Statistics and Probability · Physics 2017-09-13 Lucas Lacasa , Jacopo Iacovacci

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…

Machine Learning · Computer Science 2023-06-29 Sérgio Machado , Anirudh Sridhar , Paulo Gil , Jorge Henriques , José M. F. Moura , Augusto Santos

A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In…

Data Structures and Algorithms · Computer Science 2023-02-24 Guillaume Ducoffe , Laurent Feuilloley , Michel Habib , François Pitois

Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of…

Data Analysis, Statistics and Probability · Physics 2015-10-14 Lucas Lacasa , Ryan Flanagan

Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence…

Combinatorics · Mathematics 2015-12-18 Jonathan McLaughlin

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…

Computational Geometry · Computer Science 2013-06-14 Alexander Koch , Marcus Krug , Ignaz Rutter

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…

Social and Information Networks · Computer Science 2016-11-18 Ning Ruan , Ruoming Jin , Yan Huang

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…

Data Analysis, Statistics and Probability · Physics 2010-02-25 Bartolo Luque , Lucas Lacasa , Fernando Ballesteros , Jordi Luque

Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…

Pattern Formation and Solitons · Physics 2017-03-31 Afroza Shirin , Dionicio F. Rios , Francesco Sorrentino

In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to address the problem of recognition: for a reflexive graph G in which no two…

Combinatorics · Mathematics 2018-01-30 Mark Siggers

Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…

Machine Learning · Computer Science 2020-07-17 Carlos Lassance , Vincent Gripon , Gonzalo Mateos

A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…

Data Structures and Algorithms · Computer Science 2025-05-07 Lorenzo Balzotti