A Big Result On Graph Isomorphism

It’s not often that I see excitement from multiple friends in the world of academia. Everyone who appreciates these problems for what they are, and what solving them might bring to the world will be watching on with interest this week – including me!

Gödel's Lost Letter and P=NP

laci

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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