On the Hardness of Graph Isomorphism

  • Authors:
  • Jacobo Torán

  • Affiliations:
  • -

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

Abstract

We show that the graph isomorphism problem is hard under DLOGTIME uniform AC{$^0$} many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class {Mod}$_k$L and for the class DET of problems NC{$^1$} reducible to the determinant. These are the strongest known hardness results for the graph isomorphism problem and imply a randomized logarithmic space reduction from the perfect matching problem to graph isomorphism. We also investigate hardness results for the graph automorphism problem.