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Unsolved problems in visibility graphs of points, segments, and polygons

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TLDR
In this article, the authors present open problems and conjectures on visibility graphs of points, segments, and polygons along with necessary backgrounds for understanding them and present a survey article.
Abstract
In this survey article, we present open problems and conjectures on visibility graphs of points, segments, and polygons along with necessary backgrounds for understanding them.

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A comprehensive study on pathfinding techniques for robotics and video games

TL;DR: An overview of popular pathfinding algorithms and techniques based on graph generation problems focuses on recent developments and improvements in existing techniques and examines their impact on robotics and the video games industry.
Journal ArticleDOI

A Review of Global Path Planning Methods for Occupancy Grid Maps Regardless of Obstacle Density

TL;DR: The contribution of this work includes the definition of metrics for path planning benchmarks, actual benchmarks of the most common global path planning algorithms and an educated algorithm parameterization based on a global obstacle density coefficient.
Journal ArticleDOI

Survey of Surveys SoS - Mapping The Landscape of Survey Papers in Information Visualization

TL;DR: This paper classifies survey papers into natural topic clusters which enables readers to find relevant literature and develops the first classification of classifications.
Journal ArticleDOI

Recognition and Complexity of Point Visibility Graphs

TL;DR: It is shown that there exist point visibility graphs that do not admit any geometric realization with points on a grid, and it is proved that the problem of recognizing visibility graphs of points onA grid is decidable if and only if the existential theory of the rationals is dec formidable.
References
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Book

Graph theory

Frank Harary
Book

Graph Theory

TL;DR: Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.
Book

Computational Geometry: Algorithms and Applications

TL;DR: In this article, an introduction to computational geometry focusing on algorithms is presented, which is related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems.
Book ChapterDOI

On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities

TL;DR: This chapter reproduces the English translation by B. Seckler of the paper by Vapnik and Chervonenkis in which they gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in Soviet Mathematics Doklady.
Journal ArticleDOI

A threshold of ln n for approximating set cover

TL;DR: It is proved that (1 - o(1) ln n setcover is a threshold below which setcover cannot be approximated efficiently, unless NP has slightlysuperpolynomial time algorithms.