The Complexity of Planarity Testing

  • Eric Allender
  • Meena Mahajan
Conference paper

DOI: 10.1007/3-540-46541-3_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)
Cite this paper as:
Allender E., Mahajan M. (2000) The Complexity of Planarity Testing. In: Reichel H., Tison S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg

Abstract

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 FLSL.

Previously, these problems were known to reside in the complexity class AC1, 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].

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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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