Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity

Authors

  • David Eppstein

DOI:

https://doi.org/10.7155/jgaa.00319

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(n7/6). No known input causes our algorithm to use area Ω(n1+ϵ) for any ϵ > 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.

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Published

2014-05-01

How to Cite

Eppstein, D. (2014). Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity. Journal of Graph Algorithms and Applications, 18(2), 211–231. https://doi.org/10.7155/jgaa.00319