The Complexity of Planarity Testing

  • Eric Allender
  • Meena Mahajan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)


We clarify the computational complexity of planarity testing, by showing that planarity testing is hard for L, and lies in SL. This nearly settles the question, since it is widely conjectured that L = SL [25]. The upper bound of SL matches the lower bound of L in the context of (nonuniform) circuit complexity, since L/poly is equal to SL/poly.

Similarly, we show that a planar embedding, when one exists, can be found in FL SL.

Previously, these problems were known to reside in the complexity class AC 1, via a O(log n) time CRCW PRAM algorithm [22], although planarity checking for degree-three graphs had been shown to be in SL [23, 20].


Span Tree Planarity Testing Constraint Graph Fundamental Cycle Euler Tour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Eric Allender
    • 1
  • Meena Mahajan
    • 2
  1. 1.Dept. of Computer ScienceRutgers UniversityPiscatawayUSA
  2. 2.The Institute of Mathematical SciencesChennaiIndia

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