  We give a polynomial time reduction from vector scheduling problem (VS) to
generalized load balancing problem (GLB). This reduction gives the first
non-trivial online algorithm for VS where vectors come in an online fashion.
The online algorithm is very simple in that each vector only needs to minimize
the $L_{\ln(md)}$ norm of the resulting load when it comes, where $m$ is the
number of partitions and $d$ is the dimension of vectors. It has an
approximation bound of $e\log(md)$, which is in $O(\ln(md))$, so it also
improves the $O(\ln^2d)$ bound of the existing polynomial time algorithm for
VS. Additionally, the reduction shows that GLB does not have constant
approximation algorithms that run in polynomial time unless $P=NP$.
