  In order to provide a high resilience and to react quickly to link failures,
modern computer networks support fully decentralized flow rerouting, also known
as local fast failover. In a nutshell, the task of a local fast failover
algorithm is to pre-define fast failover rules for each node using locally
available information only. These rules determine for each incoming link from
which a packet may arrive and the set of local link failures (i.e., the failed
links incident to a node), on which outgoing link a packet should be forwarded.
Ideally, such a local fast failover algorithm provides a perfect resilience
deterministically: a packet emitted from any source can reach any target, as
long as the underlying network remains connected. Feigenbaum et al. (ACM PODC
2012) and also Chiesa et al. (IEEE/ACM Trans. Netw. 2017) showed that it is not
always possible to provide perfect resilience. Interestingly, not much more is
known currently about the feasibility of perfect resilience.
  This paper revisits perfect resilience with local fast failover, both in a
model where the source can and cannot be used for forwarding decisions. We
first derive several fairly general impossibility results: By establishing a
connection between graph minors and resilience, we prove that it is impossible
to achieve perfect resilience on any non-planar graph; furthermore, while
planarity is necessary, it is also not sufficient for perfect resilience. On
the positive side, we show that graph families closed under link subdivision
allow for simple and efficient failover algorithms which simply skip failed
links. We demonstrate this technique by deriving perfect resilience for
outerplanar graphs and related scenarios, as well as for scenarios where the
source and target are topologically close after failures.
