[praptak]

Many results about unfeasibility of computer-based solutions to some problems were not known. For example the first important results about NP-hardness come from the seventies.

I believe it wasn't even clear that the big O complexity is important in assessing how effective an algorithm is. This is pretty much obvious to us now (sometimes too obvious - there are some edge cases when the constant factor wins over the asymptotic complexity).

[scott_s]

I agree with everything you said, except the parenthetical. I have difficulty considering matrix multiplication an "edge case," and I think that it's more common than you imply for us to choose algorithms with a higher asymptotic bound because of constant factors and architectural effects (mostly caching).

[praptak]

Ok, agreed about matrix multiplication and probably a few other problems, disagreeing about cache.

You cannot really say that cache-aware algorithms have higher asymptotic bound. Some of them might happen to have below-optimal asymptotic bound in a cache-unaware memory model, which sort of misses the point of the algorithms being aware of cache.

[scott_s]

You cannot really say that cache-aware algorithms have higher asymptotic bound.

Don't worry, I'm not. I'm saying that sometimes, naive algorithms have better cache behavior than more complicated algorithms with lower asymptotic bounds.