

Don't Fall In Love With Your Model: The Cautionary Tale of my Recent proof that P=NP  - tyn
http://www.math.rutgers.edu/~zeilberg/Opinion98.html

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jibiki
The article is (obviously) a joke. But it raises an interesting point about
computation (namely, it's a small miracle that practically computable problems
are usually those with polynomial time solutions.)

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Retric
We might talk about polynomial time like that's reasonable, but few useful
algorithms are worse than X^2 * log x.

After all, the man issue is not the size of the algorithm but how long f(N)
takes and all to often we see N > 1,000,000,000 which limits what's
reasonable.

~~~
banned_man
I think matrix multiplication is O(N^2.71), and there are a few problems in
abstract algebra that have doubly exponential algorithms.

~~~
miloshh
Yes, but that is for an N x N matrix. It is more useful to express the
complexity in the size of the input, in which case matrix multiplication is
N^1.5 or better. (As far as I know, the best known algorithm is pretty close
to linear, but it's not known if a linear one exists.)

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smoofra
crackpottery

