Summary: The complexity of planarity testing
Dept. of Computer Science,
Piscataway, NJ, USA.
The Institute of Mathematical Sciences,
Chennai 600 113, INDIA.
August 25, 2003
We clarify the computational complexity of planarity testing, by showing that pla-
narity testing is hard for L, and lies in SL. This nearly settles the question, since it
is widely conjectured that L = SL [Sak96]. The upper bound of SL matches the lower
bound of L in the context of (nonuniform) circuit complexity, since L/poly is equal to
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 [RR94], although planarity checking for