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. © 1998 Springer-Verlag.
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CITATION STYLE
Barrington, D. A. M., Lu, C. J., Miltersen, P. B., & Skyum, S. (1998). Searching constant width mazes captures the AC0 hierarchy. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1373 LNCS, pp. 73–83). https://doi.org/10.1007/BFb0028550
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