Robust Routing for Dynamic Wireless Networks Based on Stable Embeddings

Routing packets is a central function of multi-hop wireless networks. Traditionally, there have been two paradigms for routing, either based on the geographical coordinates of the nodes (geographic routing), or based on the connectivity graph (topology-based routing). The former implicitly assumes that geometry determines connectivity, whereas the latter does not exploit this inherent geometry of wireless networks, and assumes a general graph instead. In this paper, we explore ideas that attempt to bridge these two paradigms. We do so by investigating routing techniques based on metric embeddings of the connectivity graph. If this graph is closely related to the underlying geometry of the nodes, then it is possible to embed the graph in a low-dimensional normed space. This keeps the overhead of the routing protocol low. We specifically explore embeddings of dynamic networks induced by channel fading and mobility. This motivates the novel problem of stable embeddings, where the additional goal is to maintain an embedding over time, such that the evolution of the embedding faithfully captures the evolution of the underlying graph itself. This is crucial to limit the control overhead of the routing protocol, and to ensure that our approach is scalable.