Why this time complexity is not a valid answer?

45 Views Asked by At

We are working on a solver for a problem having next open question:

Is possible to implement a solver for the problem in time $O(2^{(1-\epsilon) \cdot \frac{n}{2}})$, for some $\epsilon>0$

And we implemented a solver in time $O(2^{(1-\frac{4}{n}) \cdot \frac{n}{2}})$

When checking this result with the question's author, he stated this time does not answer the question without further explanation, even when $\frac{4}{n}$ is $> 0$ for all $n > 0$.

I accept his answer, but I would like to understand why is not valid so we can try a different approach that could answer the questions properly.