complexity of outputting the union of a collection of subsets of a set This question concerns the time complexity of outputting the unions of subsets of a given set.

Given $m$ subsets of an $k$-element set, can the union of those sets be computed in linear time with respect to $m+k$?  Or $(m+k)p(\log (m+k))$, where $p(x)$ is some polynomial?  Or at least known is there a  subquadratic  algorithm (with respect to $m+k$)?

Any direction on this would be much appreciated.
That's not possible.  Any correct algorithm will have to read all of the input.  The input size is $\Theta(mk)$, so that means any correct algorithm will have to have running time at least $\Omega(mk)$.  $O(m+k)$ and $O(m+k) p(\log(m+k)))$ are not achievable.