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Reductions to Graph Isomorphism

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Abstract

We show that several reducibility notions coincide when applied to the Graph Isomorphism (GI) problem. In particular we show that if a set is many-one logspace reducible to GI, then it is in fact many-one \(\textsf{AC}^{0}\) reducible to GI. For the case of Turing reducibilities we show that for any k≥0 an \(\textsf{NC}^{k+1}\) reduction to GI can be transformed into an \(\textsf{AC}^{k}\) reduction to the same problem.

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Authors and Affiliations

  1. Institut für Theoretische Informatik, Universität Ulm, 89069, Ulm, Germany

    Jacobo Torán

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  1. Jacobo Torán
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Correspondence to Jacobo Torán.

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A preliminary version of this paper appeared in the conference FSTTCS-07.

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Torán, J. Reductions to Graph Isomorphism. Theory Comput Syst 47, 288–299 (2010). https://doi.org/10.1007/s00224-008-9159-1

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  • DOI: https://doi.org/10.1007/s00224-008-9159-1

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