Given are $n$ $d$-dimensional vectors and $m$ machines where $d$ need not be fixed. The objective is to minimize the makespan i.e., assign the vectors to machines such that the maximum of the component-wise sum is minimized over all machines.
I would like to know is there any constant factor approximation algorithm for this problem and is there a generalization of list scheduling to this problem, if so what is its worst-case ratio?