Sub-exponential for Subset Sum on the total bit length of the input
This doesn't violate the exponential time hypothesis.  The exponential time hypothesis says that k-SAT takes exponential time, i.e., $\Omega(2^{cn})$ for some constant $c&gt;0$.  So if you found a $O(2^{\sqrt{n}})$ time algorithm for k-SAT, that would violate the exponential time hypothesis -- but a a $O(2^{\sqrt{n}})$ time algorithm for subset sum does not violate the hypothesis.