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