Reductions to graph isomorphism

Authors:
Jacobo Torán
Affiliations:
Institut für Theoretische Informatik, Universität Ulm, Ulm, Germany
Venue:
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Year:
2007

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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 AC0 reducible to GI. For the case of Turing reducibilities we show that for any k ≥ 0 an NCk+1 reduction to GI can be transformed into an ACk reduction to the same problem.