Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
J. Toran , Abteilung Theor. Inf., Ulm Univ., Germany
We show that the graph isomorphism problem is hard under logarithmic space many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space), for every logarithmic space modular class Mod/sub k/L and for the class DET of problems NC/sup 1/ reducible to the determinant. These are the strongest existing hardness results for the graph isomorphism problem, and imply a randomized logarithmic space reduction from the perfect matching problem to graph isomorphism.
computational complexity; encoding; graph theory; hardness; graph isomorphism; logarithmic space many-one reductions; complexity classes; probabilistic logarithmic space; determinant; hardness results; randomized logarithmic space reduction; perfect matching
J. Toran, "On the hardness of graph isomorphism," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 180.