Literary Studies
Ingo
Wegener
optimal height
plane graph G
https://doi.org/10.1007/11786986_36
bounds
paper
size
407-418
vertices
graph G
en
VR
focus
classical representation
size of VR
literature
optimal width
false
The visibility representation (VR for short) is a classical representation of plane graphs. VR has various applications and has been extensively studied in literature. One of the main focuses of the study is to minimize the size of VR. It is known that there exists a plane graph G with n vertices where any VR of G requires a size at least \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$(\lfloor \frac{2n}{3} \rfloor) \times (\lfloor \frac{4n}{3} \rfloor -3)$\end{document}.In this paper, we prove that every plane graph has a VR with height at most \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$\frac{2n}{3}+2\lceil \sqrt{n/2}\rceil$\end{document}, and a VR with width at most \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$\frac{4n}{3}+2\lceil \sqrt{n}\rceil$\end{document}. These representations are nearly optimal in the sense that they differ from the lower bounds only by a lower order additive term. Both representations can be constructed in linear time. However, the problem of finding VR with optimal height and optimal width simultaneously remains open.
additive term
chapter
lower bounds
width
Optimal Visibility Representations
problem
linear time
sense
lower order additive term
height
2006-01-01
https://scigraph.springernature.com/explorer/license/
main focus
plane graph
visibility representation
2022-01-01T19:17
Nearly Optimal Visibility Representations of Plane Graphs
chapters
graph
applications
time
2006
study
order additive term
terms
representation
978-3-540-35904-3
978-3-540-35905-0
Automata, Languages and Programming
Zhang
Huaming
Springer Nature
He
Xin
Bugliesi
Michele
doi
10.1007/11786986_36
Springer Nature - SN SciGraph project
Department of Computer Science and Engineering, SUNY at Buffalo, 14260, Buffalo, NY, USA
Department of Computer Science and Engineering, SUNY at Buffalo, 14260, Buffalo, NY, USA
Sassone
Vladimiro
Bart
Preneel
Computer Science Department, University of Alabama in Huntsville, 35899, Huntsville, AL, USA
Computer Science Department, University of Alabama in Huntsville, 35899, Huntsville, AL, USA
Language, Communication and Culture
pub.1017247286
dimensions_id