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Logspace Reduction of Directed Reachability for Bounded Genus Graphs to the Planar Case

Published:01 March 2010Publication History
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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. [2009] 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.

References

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  1. Logspace Reduction of Directed Reachability for Bounded Genus Graphs to the Planar Case

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        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 1, Issue 3
        March 2010
        64 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/1714450
        Issue’s Table of Contents

        Copyright © 2010 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 March 2010
        • Revised: 1 December 2009
        • Accepted: 1 December 2009
        • Received: 1 June 2009
        Published in toct Volume 1, Issue 3

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