Drawing Arrangement Graphs in Small Grids, or How to Play Planarity

  • David Eppstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)


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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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • David Eppstein
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaIrvineUSA

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