Suppose given $k$-sorted arrays of numbers that contains total of $n$ elements. we try to choose $k$ elements in $k$ arrays (each arrays exactly one element) such that minimize difference between maximum and minimum number in chosen $k$ numbers. What is lower bound of this problem? I have an algorithm that solve above problem in $\Omega(n\log k)$.
I think this problem related to $k$-way merge. And already I know why the lower bound of $k$-way merge is $\Omega(n\log k)$. But I can't reduce $k$-way merge to above problem.