Abstract
There has been a great deal of progress in the fifteen years that have elapsed since Wigderson published his survey on the complexity of the graph connectivity problem [Wig92]. Most significantly, Reingold solved the longstanding question of the complexity of the s-t connectivity problem in undirected graphs, showing that this is complete for logspace (L) [Rei05].
This survey talk will focus on some of the remaining open questions dealing with graph reachability problems. Particular attention will be paid to these topics:
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Reachability in planar directed graphs (and more generally, in graphs of low genus) [ADR05, BTV07].
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Reachability in different classes of grid graphs [ABC + 06].
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Reachability in mangroves [AL98].
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Allender, E. (2007). Reachability Problems: An Update. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_3
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