Planarity, Exclusivity, and Unambiguity

We provide new upper bounds on the complexity of the s-t-connectivity problem in planar graphs, thereby providing additional evidence that this problem is not complete for NL. This also yields a new upper bound on the complexity of computing edit distance. Building on these techniques, we provide new upper bounds on the complexity of several other computational problems on planar graphs. All of these problems are shown to be solvable in logarithmic time on a concurrent-read exclusive-write (CREW) PRAM. The new upper bounds are provided by making use of a known characterization of CREW algorithms in terms of “unambiguous” AC circuits. This seems to be the first occasion where this characterization has been used in order to provide new upper bounds on natural problems. *Department of Computer Science, Rutgers University, Piscataway, NJ, USA, allender@cs.rutgers.edu. Supported by NSF grant CCF-1514164. This work was done in part while the author was visiting the Simons Institute for the Theory of Computing. „CMI, Chennai, India, archit@cmi.ac.in. Partially supported by a grant from Infosys foundation. …CMI, Chennai, India, sdatta@cmi.ac.in. Partially supported by a grant from Infosys foundation and SERB grant MTR/2017/000480. §CMI, Chennai, India, anish343@gmail.com. Partially supported by a grant from Infosys foundation and TCS PhD fellowship.

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