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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Eppstein, D. (2013). Drawing Arrangement Graphs in Small Grids, or How to Play Planarity. In: Wismath, S., Wolff, A. (eds) Graph Drawing. GD 2013. Lecture Notes in Computer Science, vol 8242. Springer, Cham. https://doi.org/10.1007/978-3-319-03841-4_38
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DOI: https://doi.org/10.1007/978-3-319-03841-4_38
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