NoN-Greedy Routing Algorithms Are Optimal or Know thy Neighbor’s Neighbor

Greedy routing is a common approach when a graph has some underlying metric. We present an approach for designing routing algorithms called NoN-Greedy (Neighbor-of-Neighbor). We show that in two settings it reduces significantly the number of hops taken before the destination is reached and can yield degree optimal routing (in a network of degree O(log n) this means O(log / log logn) hops). In particular we consider the skip-graph peer-to-peer network and the small world settings and show that both models indeed permit degree optimal routing. The theoretic results are backed by simulations which show a significant improvement. While not being Greedy per-se, the NoN-Greedy algorithm preserves some good properties of greedy algorithms. Furthermore we show a lower bound proving that in order to reduce the number of hops, information regarding neighbors only is insufficient, thus the NoN approach is essential.