Searching Constant Width Mazes Captures the

Hierarchy

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

September 1997

Abstract:

We show that searching a width k maze is complete for , i.e., for the k'th level of the hierarchy. Equivalently, st-connectivity for width k grid graphs is complete for . As an application, we show that there is a data structure solving dynamic st-connectivity for constant width grid graphs with time bound 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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