Space lower bounds for low-stretch greedy embeddings

摘要

Greedy (geometric) routing is an important paradigm for routing in communication networks. It uses an embedding of the nodes of a network into points of a space (e.g., R-d) equipped with a distance function (e.g., the Euclidean distance l(2)) and uses as address of each node the coordinates of the corresponding point. The embedding has particular properties so that the routing decision for a packet is taken greedily based only on the addresses of the current node, its neighbors, and the destination node and the distances of the corresponding points. In this way, there is no need to keep extensive routing information (e.g., routing tables) at the nodes. Embeddings that allow for this functionality are called greedy embeddings. Even though greedy embeddings do exist for several spaces and distance functions, they usually result in paths of high stretch, i.e., significantly longer than the corresponding shortest paths.