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41st Annual Symposium on Foundations of Computer Science
On the hardness of graph isomorphism
Redondo Beach, California
November 12-November 14
ISBN: 0-7695-0850-2
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.
Index Terms:
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," focs, pp.180, 41st Annual Symposium on Foundations of Computer Science, 2000
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