BibTeX
@MISC{Allender_reachabilityproblems:,
author = {Eric Allender},
title = {Reachability Problems: An Update},
year = {}
}
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Abstract
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: – Reachability in planar directed graphs (and more generally, in graphs of low genus) [ADR05,BTV07]. – Reachability in different classes of grid graphs [ABC + 06]. – Reachability in mangroves [AL98]. The problem of finding a path from one vertex to another in a graph is the first problem that was identified as being complete for a natural subclass of P; it was shown to be complete for nondeterministic logspace (NL) by Jones [Jon75]. Restricted versions of this problem were subsequently shown to be complete for other natural complexity
Keyphrases
reachability problem natural subclass natural complexity first problem survey talk great deal grid graph abc longstanding question s-t connectivity problem fifteen year particular attention low genus nondeterministic logspace jones jon75 graph connectivity problem wig92 open question different class undirected graph graph reachability problem
