Reachibility between first and last layer in grid graph in logspace
I can't post a comment, which would be more appropriate:

Reingold's result gives a logspace algorithm, but reachability on undirected grid graphs was show to be in $L$ by Blum and Kozen about 30 years prior:

M. Blum and D. Kozen. On the power of the compass (or,
why mazes are easier to search than graphs). In IEEE Symposium
on Foundations of Computer Science (FOCS), pages
132–142, 1978.