# divisibility.wordpress.com

## math blog

Collecting a few results from previous posts which, when taken together, seem to imply the results in the “germs” post hold more general when globalized (so for instance you could run the log-MMP in a family of surfaces over $\mathbb{Z}$ .)

MMAT0.1     12/3/2015 (probably reasonably complete version)

I thought GI was supposed to be harder than factoring! yikes

Lszl Babai is one of the world experts on complexity theory, especially related to groups and graphs. He also recently won the 2015 ACM Knuth Prize, for which we congratulate him.

Today we wish to discuss a new result that he has announced that will place graph isomorphism almost in polynomial time.

More exactly Lszl shows that Graph Isomorphism is in Quasipolynomial Time: that is time of the form

\$latex displaystyle 2^{O(log(n))^{c}}, &fg=000000\$

for some constant \$latex {c}&fg=000000\$. Polynomial time is the case when \$latex {c=1}&fg=000000\$, but any \$latex {c}&fg=000000\$ is a huge improvement over the previous best result.

Luca Trevisan already has made a post on this result, and Scott Aaronson likewise. Luca further promises to be in Chicago next Tuesday when Lszl gives his talk on the result—here is the abstract of the talk:

We outline an algorithm that solves the Graph Isomorphism (GI) problem and the…

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