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TR09-050 | 28th May 2009 00:00
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#### Logspace reduction of directed reachability for bounded genus graphs to the planar case

**Abstract:**
Directed reachability (or briefly reachability) is the following decision problem: given a directed graph G and two of its vertices s,t, determine whether there is a directed path from s to t in G. Directed reachability is a standard complete problem for the complexity class NL. Planar reachability is an important restricted version of the reachability problem, where the input graph is planar. Planar reachability is hard for L and is contained in NL but is not known to be NL-complete or contained in L. Allender et al. showed that reachability for graphs embedded on the torus is logspace-reducible to the planar case. We generalize this result to graphs embedded on a fixed surface of arbitrary genus.