Let $f$ be a probability density function of the form $$ f(x)=k \times g(x), $$ where $k$ is the normalizing constant, $g(x)$ is the kernel of the distribution, that is the part which involves $x$, $g(x)$ typically is not simple, in the sense that integrals involving it are not analytically treatable.
There are many approximate methods for simulating from such a probability distribution, most of them requires only the kernel of the distribution: acceptance-rejection, metropolis-hastings, etc.
My question:
But, if I know $k$, which method(s) would be the most (time) efficient to generate random number from $f$?
For example, from acceptance-rejection and metropolis-hastings perspective, knowing $k$ makes no difference. A more straightforward approach that would take advantage of $k$ would be the inverse transform sampling (https://en.wikipedia.org/wiki/Inverse_transform_sampling), however if $g(x)$ is complicate we will not be able to find the corresponding cdf $F(x)=P(X\leq x)$ or, even if we can, the inversion might no be possible, so this method is off of the table(?).
Any other method that would take advantage of this situation? thanks in advance.