I have this problem:
Given a set of unit vectors $\{ \vec{v_i} \}$, I want to determine another set, $W$, the element of which are in $\{ \vec{v_i} \}$(repeating allowed), so that the module of the sum of all the vectors in W is minimized. The size of $W$ is $n$, a fixed integer.
And what if the elements in $\{ \vec{v_i} \}$ are not necessarily unit vectors?
Can you please give me any ideas to solve this? I guess it's an NP problem but I cannot prove it. Thanks!