We study complexity and algorithms for network updates in the setting of Software Defined Networks. Our focus lies on consistent updates for the case of updating forwarding rules in a loop free manner and the migration of flows without congestion. In both cases, we study how the power of two affects the respective problem setting. For loop freedom, we show that scheduling consistent updates for two destinations is NP-hard for a sublinear number of rounds. We also consider the dynamic case, and show that this problem is NP-hard as well via a reduction from Feedback Arc Set. While the power of two increases the complexity for loop freedom, the converse is true when allowing to split flows twice. For the NP-hard problem of consistently migrating unsplittable flows to new routes while respecting waypointing and service chains, we prove that two-splittability allows the problem to be tractable again.

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