Greedy Routing and Its Algebra in Geographic Routing

In this paper, we propose a novel routing algebra system to investigate greedy routing in geographic routing. Four important algebraic properties, respectively named mutex, transition, source independence and strict preference, are defined in this algebra system. Based on these algebraic properties, the necessary and sufficient conditions for the loop-free and consistent compatibilities of greedy routing based routing protocols are derived. The application of this proposed algebra is illustrated with existing different greedy routings in geographic routing. In theory, our work provides essential criterions for evaluating and designing greedy routing based routing protocols.