On Greedy Routing in Degree-bounded Graphs over d-Dimensional Internet Coordinate Embeddings

In this paper we will introduce a new d-dimensional graph for constructing geometric application layer overlay net-works. Our approach will use internet coordinates, embedded using the L∞ -metric. After describing the graph structure, we will show how it limits maintenance overhead by bounding each node’s out-degree and how it supports greedy routing using one-hop neighbourhood information in each routing step. We will further show that greedy routing can always compute a path in our graph and we will also prove that in each forwarding step the next hop is closer to the destination than the current node.