The document discusses guaranteed greedy routing in overlay networks. It proposes constructing an overlay network using a Nearest Neighbors Convex Set (NNCS) that guarantees nodes will always have a neighbor closer to the destination. This allows for greedy routing to make progress at each hop. The NNCS is constructed by dividing the virtual space around each node into half-spaces defined by its neighbors. Various applications like multicast trees, service discovery, and spatially-bound querying can take advantage of the NNCS approach. Evaluation shows the NNCS outperforms Pastry in terms of relative path stretch.