A 2-Approximation for the Height of Maximal Outerplanar Graph Drawings
Data Structures and Algorithms
2017-02-07 v1 Computational Geometry
Abstract
In this paper, we study planar drawings of maximal outerplanar graphs with the objective of achieving small height. A recent paper gave an algorithm for such drawings that is within a factor of 4 of the optimum height. In this paper, we substantially improve the approximation factor to become 2. The main ingredient is to define a new parameter of outerplanar graphs (the so-called umbrella depth, obtained by recursively splitting the graph into graphs called umbrellas). We argue that the height of any poly-line drawing must be at least the umbrella depth, and then devise an algorithm that achieves height at most twice the umbrella depth.
Cite
@article{arxiv.1702.01719,
title = {A 2-Approximation for the Height of Maximal Outerplanar Graph Drawings},
author = {Therese Biedl and Philippe Demontigny},
journal= {arXiv preprint arXiv:1702.01719},
year = {2017}
}