On the Hardness of Graph Isomorphism

We show that the graph isomorphism problem is hard under DLOGTIME uniform AC0 many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class ModkL and for the class DET of problems NC1 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. Key words. AUTHOR MUST PROVIDE AMS subject classifications. AUTHOR MUST PROVIDE DOI. 10.1137/S009753970241096X

• Type: Conference
• Year: 2000
• Where: FOCS
• Authors: Jacobo Torán
• Keywords: FOCS 2000, Graph Isomorphism Problem, Logarithmic Space, Probabilistic Logarithmic Space, Theoretical Computer Science