  In the weighted load balancing problem, the input is an $n$-vertex bipartite
graph between a set of clients and a set of servers, and each client comes with
some nonnegative real weight. The output is an assignment that maps each client
to one of its adjacent servers, and the load of a server is then the sum of the
weights of the clients assigned to it. The goal is to find an assignment that
is well-balanced, typically captured by (approximately) minimizing either the
$\ell_\infty$- or $\ell_2$-norm of the server loads. Generalizing both of these
objectives, the all-norm load balancing problem asks for an assignment that
approximately minimizes all $\ell_p$-norm objectives for $p \ge 1$, including
$p = \infty$, simultaneously.
  Our main result is a deterministic $O(\log{n})$-pass $O(1)$-approximation
semi-streaming algorithm for the all-norm load balancing problem. Prior to our
work, only an $O(\log{n})$-pass $O(\log{n})$-approximation algorithm for the
$\ell_\infty$-norm objective was known in the semi-streaming setting.
  Our algorithm uses a novel application of the multiplicative weights update
method to a mixed covering/packing convex program for the all-norm load
balancing problem involving an infinite number of constraints.
