What is an asymptotically tight upper bound?
Saying that a big-O bound is "asymptotically tight" basically means that the author should have written $\Theta(-)$.  For example, $O(x^2)$ means that it's no more than some constant times&nbsp;$x^2$ for all large enough&nbsp;$x$; "asymptotically tight" means it really is some constant times&nbsp;$x^2$ for large enough&nbsp;$x$ and not, say, some constant times&nbsp;$x^{1.999}$.