  The software-defined networking paradigm introduces interesting opportunities
to operate networks in a more flexible, optimized, yet formally verifiable
manner. Despite the logically centralized control, however, a Software-Defined
Network (SDN) is still a distributed system, with inherent delays between the
switches and the controller. Especially the problem of changing network
configurations in a consistent manner, also known as the consistent network
update problem, has received much attention over the last years. In particular,
it has been shown that there exists an inherent tradeoff between update
consistency and speed. This paper revisits the problem of updating an SDN in a
transiently consistent, loop-free manner. First, we rigorously prove that
computing a maximum (greedy) loop-free network update is generally NP-hard;
this result has implications for the classic maximum acyclic subgraph problem
(the dual feedback arc set problem) as well. Second, we show that for special
problem instances, fast and good approximation algorithms exist.
