Know thy neighbor's neighbor: the power of lookahead in randomized P2P networks

Several peer-to-peer networks are based upon randomized graph topologies that permit efficient greedy routing, e.g., randomized hypercubes, randomized Chord, skip-graphs and constructions based upon small-world percolation networks. In each of these networks, a node has out-degree Θ(log n), where n denotes the total number of nodes, and greedy routing is known to take O(log n) hops on average. We establish lower-bounds for greedy routing for these networks, and analyze Neighbor-of-Neighbor (NoN)-greedy routing. The idea behind NoN, as the name suggests, is to take a neighbor’s neighbors into account for making better routing decisions. The following picture emerges: Deterministic routing networks like hypercubes and Chord have diameter Θ(log n) and greedy routing is optimal. Randomized routing networks like randomized hypercubes, randomized Chord, and constructions based on small-world percolation networks, have diameter Θ(log n/ log log n) with high probability. The expected dia...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Gurmeet Singh Manku, Moni Naor, Udi Wieder
• Keywords: Algorithms, Greedy Routing, Randomized, Small-world Percolation Networks, STOC 2004