  Social Overlays suffer from high message delivery delays due to insufficient
routing strategies. Limiting connections to device pairs that are owned by
individuals with a mutual trust relationship in real life, they form topologies
restricted to a subgraph of the social network of their users. While
centralized, highly successful social networking services entail a complete
privacy loss of their users, Social Overlays at higher performance represent an
ideal private and censorship-resistant communication substrate for the same
purpose.
  Routing in such restricted topologies is facilitated by embedding the social
graph into a metric space. Decentralized routing algorithms have up to date
mainly been analyzed under the assumption of a perfect lattice structure.
However, currently deployed embedding algorithms for privacy-preserving Social
Overlays cannot achieve a sufficiently accurate embedding and hence
conventional routing algorithms fail. Developing Social Overlays with
acceptable performance hence requires better models and enhanced algorithms,
which guarantee convergence in the presence of local optima with regard to the
distance to the target.
  We suggest a model for Social Overlays that includes inaccurate embeddings
and arbitrary degree distributions. We further propose NextBestOnce, a routing
algorithm that can achieve polylog routing length despite local optima. We
provide analytical bounds on the performance of NextBestOnce assuming a
scale-free degree distribution, and furthermore show that its performance can
be improved by more than a constant factor when including Neighbor-of-Neighbor
information in the routing decisions.
