On the necessity of using Delaunay Triangulation substrate in greedy routing based networks

Large scale decentralized communication systems have motivated a new trend towards online routing where routing decisions are performed based on a limited and localized knowledge of the network. Geometrical greedy routing has been among the simplest and most common online routing schemes. While a geometrical online routing scheme is expected to deliver each packet to the point in the network that is closest to the destination, geometrical greedy routing, when applied over generalized substrate graphs, does not guarantee such delivery as its forwarding decision might deliver packets to a localized minimum instead. This letter investigates the necessary and sufficient conditions of greedy supporting graphs that would guarantee such delivery when used as a greedy routing substrate.