I am trying to find which of following algorithms has the smallest running time:
1) $O\left(\sqrt{q}\cdot\operatorname{polylog}(q)\right)$; is that linearithmic?
2) $O\left(\operatorname{polylog}(q)\cdot\max\{\sqrt{p}\}\right)$; is that linearithmic?
3) $2^{O\left(\sqrt{n \log(n)}\right)}$; is that polynomial?
Can you help me?