Succinct Greedy Geometric Routing Using Hyperbolic Geometry

We describe a method for performing greedy geometric routing for any n-vertex simple connected graph G in the hyperbolic plane, so that a message M between any pair of vertices may be routed by having each vertex that receives M pass it to a neighbor that is closer to M's destination. Our algorithm produces succinct embeddings, where vertex positions are represented using O(\log n) bits and distance comparisons may be performed efficiently using these representations. These properties are useful, for example, for routing in sensor networks, where storage and bandwidth are limited.