Searching constant width mazes captures the AC0 hierarchy

  • David A. Mix Barrington
  • Chi-Jen Lu
  • Peter Bro Miltersen
  • Sven Skyum
Complexity I

DOI: 10.1007/BFb0028550

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1373)
Cite this paper as:
Barrington D.A.M., Lu CJ., Miltersen P.B., Skyum S. (1998) Searching constant width mazes captures the AC0 hierarchy. In: Morvan M., Meinel C., Krob D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg

Abstract

We show that searching a width k maze is complete for Πk, i.e., for the k'th level of the AC0 hierarchy. Equivalently, st-connectivity for width k grid graphs is complete for Πk. As an application, we show that there is a data structure solving dynamic st-connectivity for con stant width grid graphs with time bound O(log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools.

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • David A. Mix Barrington
    • 1
  • Chi-Jen Lu
    • 1
  • Peter Bro Miltersen
    • 2
  • Sven Skyum
    • 2
  1. 1.Computer Science DepartmentUniversity of MassachusettsUSA
  2. 2.BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer ScienceUniversity of AarhusUSA

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