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arXiv · 1308.0066

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

David Eppstein
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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 Ω(n^{1+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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David Eppstein. 2013-07-31. Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity. https://doi.org/10.7155/jgaa.00319

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