The submodular Santa Claus problem

as to maximize the minimum total value any player receives. This problem
is sometimes dubbed the Santa Claus problem and its different variants
have been subject to extensive research towards approximation algorithms
over the past two decades.

In the case where each player has a potentially different additive
valuation function, Chakrabarty, Chuzhoy, and Khanna [FOCS'09] gave an
O(n^{\eps};)-approximation algorithm with polynomial running time for any
constant \eps > 0 and a polylogarithmic approximation algorithm in
quasi-polynomial time. We show that the same can be achieved for monotone
submodular valuation functions, improving over the previously best
algorithm due to Goemans, Harvey, Iwata, and Mirrokni [SODA'09].