NextBestOnce: Achieving Polylog Routing despite Non-greedy Embeddings

Abstract: 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.