  The Quickest Transshipment Problem is to route flow as quickly as possible
from sources with supplies to sinks with demands in a network with capacities
and transit times on the arcs. It is of fundamental importance for numerous
applications in areas such as logistics, production, traffic, evacuation, and
finance. More than 25 years ago, Hoppe and Tardos presented the first
(strongly) polynomial-time algorithm for this problem. Their approach, as well
as subsequently derived algorithms with strongly polynomial running time, are
hardly practical as they rely on parametric submodular function minimization
via Megiddo's method of parametric search. The main contribution of this paper
is a considerably faster algorithm for the Quickest Transshipment Problem that
instead employs a subtle extension of the Discrete Newton Method. This improves
the previously best known running time of $\tilde{O}(m^4k^{14})$ to $\tilde
O(m^2k^5+m^3k^3+m^3n)$, where $n$ is the number of nodes, $m$ the number of
arcs, and $k$ the number of sources and sinks.
