Searching constant width mazes captures the AC0 hierarchy
- 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
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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