Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity
Computational Geometry
2015-07-16 v1
Abstract
We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any \epsilon>0; finding such an input would represent significant progress on the famous k-set problem from discrete geometry. Drawing line arrangement graphs is the main task in the Planarity puzzle.
Keywords
Cite
@article{arxiv.1308.0066,
title = {Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity},
author = {David Eppstein},
journal= {arXiv preprint arXiv:1308.0066},
year = {2015}
}
Comments
12 pages, 8 figures. To appear at 21st Int. Symp. Graph Drawing, Bordeaux, 2013