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Electronic Colloquium on Computational Complexity

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Reports tagged with grid graphs:
TR97-044 | 26th September 1997
David Mix Barrington, Chi-Jen Lu, Peter Bro Miltersen, Sven Skyum

Searching constant width mazes captures the AC^0 hierarchy

We show that searching a width k maze is complete for \Pi_k, i.e., for
the k'th level of the AC^0 hierarchy. Equivalently, st-connectivity
for width k grid graphs is complete for \Pi_k. As an application,
we show that there is a data structure solving dynamic st-connectivity
for constant ... more >>>

TR05-148 | 6th December 2005
Eric Allender, Samir Datta, Sambuddha Roy

The Directed Planar Reachability Problem

Revisions: 1

We investigate the s-t-connectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspace-reducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to ... more >>>

TR05-149 | 7th December 2005
Eric Allender, David Mix Barrington, Tanmoy Chakraborty, Samir Datta, Sambuddha Roy

Grid Graph Reachability Problems

Revisions: 1

We study the complexity of restricted versions of st-connectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since
* reachability on grid graphs is logspace-equivalent to reachability in general planar digraphs, and
* reachability on certain classes of grid graphs gives ... more >>>

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