## Know thy Neighbor's Neighbor: the Power of Lookahead in Randomized P2P Networks (2004)

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Venue: | In Proceedings of the 36th ACM Symposium on Theory of Computing (STOC |

Citations: | 89 - 5 self |

### BibTeX

@INPROCEEDINGS{Manku04knowthy,

author = {Gurmeet Singh Manku and Moni Naor and Udi Wieder},

title = {Know thy Neighbor's Neighbor: the Power of Lookahead in Randomized P2P Networks},

booktitle = {In Proceedings of the 36th ACM Symposium on Theory of Computing (STOC},

year = {2004},

pages = {54--63}

}

### Years of Citing Articles

### OpenURL

### Abstract

Several peer-to-peer networks are based upon randomized graph topologies that permit e#cient 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 #(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.

### Citations

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(Show Context)
Citation Context ...routing: randomized-hypercube [15, 8], randomized-Chord [15, 36], and skip-graphs [4] (also known as SkipNet [17]). Randomized-Chord is a variation on a deterministic P2P routing network called Chord =-=[34, 14]. Ski-=-p1 According to Barabási [5] this idea may have its origins in a short story “Chains” by the Hungarian writer Frigyes Karinthy from 1929; this idea has been retold and recast many times since the... |

2699 | A scalable content-addressable network
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Citation Context ...categories – deterministic and randomized. Deterministic P2P networks are based upon classical parallel inter-connection networks like hypercubes [32, 37], its variants [34], multi-dimensional meshe=-=s [31] a-=-nd de Bruijn graphs [18, 12, 25, 1, 20]. Randomized P2P networks include Viceroy [21] (a randomized emulation of butterfly networks), Symphony [23] (an adaptation of Kleinberg’s construction [19]), ... |

1424 | Pastry: Scalable, decentralized object location, and routing for large-scale peer-to-peer systems
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Citation Context ...y. Broadly, these networks can be classified into two categories – deterministic and randomized. Deterministic P2P networks are based upon classical parallel inter-connection networks like hypercube=-=s [32, 37]-=-, its variants [34], multi-dimensional meshes [31] and de Bruijn graphs [18, 12, 25, 1, 20]. Randomized P2P networks include Viceroy [21] (a randomized emulation of butterfly networks), Symphony [23] ... |

809 |
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Citation Context ...g of social networks, it is interesting to check whether people use the NoNGreedy algorithm when they navigate in a social network. Recently Dodds et al [11] repeated the famous experiment by Milgram =-=[24]-=- in which letters were passed between random nodes on a social network where edges corresponds to say, an acquaintance known by first name. In [11] people were given a target and were asked to forward... |

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Citation Context ...xamples of such graphs include social acquaintanceship networks, electric power grids, telephone call graphs, neural wiring of worms and influence networks. Models such as those by Watts and Strogatz =-=[35] are chara-=-cterized by a successful mixture of regularity and randomness to faithfully reproduce three statistical properties: the “characteristic path length”, the “average vertex degree” and the “clu... |

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Citation Context ...ir coins and setting Xi = 1 if all coins turned up to be 1. Now we have clog n fair coins, and if less than 3 of the coins 4 turned up to be 1 the algorithm will not fail. The standard Chernoff bound =-=[9] s-=-hows there is a constant c such that this happens with probability at least 1 − 1 n2d . The proof of Theorem 2.2 is now completed by combining Lemma 2.3 which handled the first phase of the routing,... |

625 | The Small-World Phenomenon: An Algorithmic Perspective
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Citation Context ...gets only through acquaintances. Milgram’s experiments, and a work by Pool and Kochen [29] confirmed that random pairs of individuals are indeed connected by short chains. As was noticed by Kleinber=-=g [19], -=-Milgram’s experiments also demonstrated that individuals are able to route messages to unknown targets.. To model the routing aspects of the Small-World Phenomenon, Kleinberg constructed a family of... |

443 | Tapestry: A resilient global-scale overlay for service deployment
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Citation Context ...y. Broadly, these networks can be classified into two categories – deterministic and randomized. Deterministic P2P networks are based upon classical parallel inter-connection networks like hypercube=-=s [32, 37]-=-, its variants [34], multi-dimensional meshes [31] and de Bruijn graphs [18, 12, 25, 1, 20]. Randomized P2P networks include Viceroy [21] (a randomized emulation of butterfly networks), Symphony [23] ... |

361 | Secure routing for structured peer-to-peer overlay networks
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Citation Context ... been shown to be O( log2 n k ) both by Manku et al [23] and by Aspnes et al [3]. Recently, three more randomized P2P networks have been devised, all of which use greedy routing: randomized-hypercube =-=[15, 8],-=- randomized-Chord [15, 36], and skip-graphs [4] (also known as SkipNet [17]). Randomized-Chord is a variation on a deterministic P2P routing network called Chord [34, 14]. Skip1 According to Barabási... |

354 |
2002): Linked: The New Science of Networks
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(Show Context)
Citation Context ... randomized-Chord [15, 36], and skip-graphs [4] (also known as SkipNet [17]). Randomized-Chord is a variation on a deterministic P2P routing network called Chord [34, 14]. Skip1 According to Barabási=-= [5] thi-=-s idea may have its origins in a short story “Chains” by the Hungarian writer Frigyes Karinthy from 1929; this idea has been retold and recast many times since then, in the literature, popular pre... |

322 | lists: A probabilistic alternative to balanced trees
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Citation Context ... Karinthy from 1929; this idea has been retold and recast many times since then, in the literature, popular press as well as scientific studies.sgraphs build upon the intuition inherent in skip-lists =-=[30].-=- All of these networks have Θ(log n) out-going links per node. greedy routing is known to take O(log n) hops on average. Among the various P2P routing networks, skip-graphs are unique in that node id... |

296 | Viceroy: a scalable and dynamic emulation of the butterfly
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- 2002
(Show Context)
Citation Context ...assical parallel inter-connection networks like hypercubes [32, 37], its variants [34], multi-dimensional meshes [31] and de Bruijn graphs [18, 12, 25, 1, 20]. Randomized P2P networks include Viceroy =-=[21] (-=-a randomized emulation of butterfly networks), Symphony [23] (an adaptation of Kleinberg’s construction [19]), randomized-hypercubes [15, 8], randomizedChord [36, 15], and a combination of Kleinberg... |

285 | SkipNet: a scalable overlay network with practical locality properties
- Harvey, Jones, et al.
- 2003
(Show Context)
Citation Context ...]. Recently, three more randomized P2P networks have been devised, all of which use greedy routing: randomized-hypercube [15, 8], randomized-Chord [15, 36], and skip-graphs [4] (also known as SkipNet =-=[17]). Ra-=-ndomized-Chord is a variation on a deterministic P2P routing network called Chord [34, 14]. Skip1 According to Barabási [5] this idea may have its origins in a short story “Chains” by the Hungari... |

247 | The impact of DHT routing geometry on resilience and proximity
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- 2003
(Show Context)
Citation Context ... been shown to be O( log2 n k ) both by Manku et al [23] and by Aspnes et al [3]. Recently, three more randomized P2P networks have been devised, all of which use greedy routing: randomized-hypercube =-=[15, 8],-=- randomized-Chord [15, 36], and skip-graphs [4] (also known as SkipNet [17]). Randomized-Chord is a variation on a deterministic P2P routing network called Chord [34, 14]. Skip1 According to Barabási... |

239 | Skip graphs
- Aspnes, Shah
- 2003
(Show Context)
Citation Context ...[23] and by Aspnes et al [3]. Recently, three more randomized P2P networks have been devised, all of which use greedy routing: randomized-hypercube [15, 8], randomized-Chord [15, 36], and skip-graphs =-=[4] -=-(also known as SkipNet [17]). Randomized-Chord is a variation on a deterministic P2P routing network called Chord [34, 14]. Skip1 According to Barabási [5] this idea may have its origins in a short s... |

170 | Symphony: Distributed Hashing in a Small World
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(Show Context)
Citation Context ...ut-going link which takes it closest to the destination. Barrière et al [6] showed that greedy routing requires Ω(log 2 n) hops for Kleinberg’s construction. Randomized Peer-to-Peer Networks Symp=-=hony [23] i-=-s a successful adaptation of Kleinberg’s construction [19] to arrive at a randomized P2P routing network. The idea is to place nodes in a ring (instead of a 2D grid) and to equip each node with mult... |

143 | Novel architectures for p2p applications: The continuous-discrete approach
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(Show Context)
Citation Context ... and randomized. Deterministic P2P networks are based upon classical parallel inter-connection networks like hypercubes [32, 37], its variants [34], multi-dimensional meshes [31] and de Bruijn graphs =-=[18, 12, 25, 1, 20]. -=-Randomized P2P networks include Viceroy [21] (a randomized emulation of butterfly networks), Symphony [23] (an adaptation of Kleinberg’s construction [19]), randomized-hypercubes [15, 8], randomized... |

141 | Random graph models of social networks
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(Show Context)
Citation Context ... a successful mixture of regularity and randomness to faithfully reproduce three statistical properties: the “characteristic path length”, the “average vertex degree” and the “clustering coe=-=fficient” [28]. -=-An important property ignored by these models is the existence of short routes, i.e., the small-world phenomenon. Kleinberg’s construction [19] aims to incorporate routing properties into random gra... |

113 | An experimental study of search in global social networks
- Dodds, Muhamad, et al.
(Show Context)
Citation Context ...of analyzing small-world graphs was the modeling of social networks, it is interesting to check whether people use the NoNGreedy algorithm when they navigate in a social network. Recently Dodds et al =-=[11]-=- repeated the famous experiment by Milgram [24] in which letters were passed between random nodes on a social network where edges corresponds to say, an acquaintance known by first name. In [11] peopl... |

104 | Graph-theoretic analysis of structured peerto-peer systems: routing distances and fault resilience - LOGUINOV, KUMAR, et al. |

89 |
Koorde: A Simple Degree-optimal Hash Table
- Kaashoek, Karger
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(Show Context)
Citation Context ... and randomized. Deterministic P2P networks are based upon classical parallel inter-connection networks like hypercubes [32, 37], its variants [34], multi-dimensional meshes [31] and de Bruijn graphs =-=[18, 12, 25, 1, 20]. -=-Randomized P2P networks include Viceroy [21] (a randomized emulation of butterfly networks), Symphony [23] (an adaptation of Kleinberg’s construction [19]), randomized-hypercubes [15, 8], randomized... |

80 | Efficient Routing in Networks with Long Range Contacts
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(Show Context)
Citation Context ...is O(log 2 n) hops, w.h.p. Local knowledge available to a node suffices for greedy routing – a message is forwarded along that out-going link which takes it closest to the destination. Barrière et =-=al [6] showe-=-d that greedy routing requires Ω(log 2 n) hops for Kleinberg’s construction. Randomized Peer-to-Peer Networks Symphony [23] is a successful adaptation of Kleinberg’s construction [19] to arrive ... |

60 | Fault-tolerant routing in peer-to-peer systems
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(Show Context)
Citation Context ...D grid) and to equip each node with multiple “longdistance” links (instead of one). The average length of greedy routes has been shown to be O( log2 n k ) both by Manku et al [23] and by Aspnes et=-= al [3]-=-. Recently, three more randomized P2P networks have been devised, all of which use greedy routing: randomized-hypercube [15, 8], randomized-Chord [15, 36], and skip-graphs [4] (also known as SkipNet [... |

54 |
Contacts and influence
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Citation Context ... the phenomenon started with Milgram’s [24] experiments in 1960’s, asking people to send letters to unfamiliar targets only through acquaintances. Milgram’s experiments, and a work by Pool and K=-=ochen [29] c-=-onfirmed that random pairs of individuals are indeed connected by short chains. As was noticed by Kleinberg [19], Milgram’s experiments also demonstrated that individuals are able to route messages ... |

52 | A generic scheme for building overlay networks in adversarial scenarios
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(Show Context)
Citation Context ... and randomized. Deterministic P2P networks are based upon classical parallel inter-connection networks like hypercubes [32, 37], its variants [34], multi-dimensional meshes [31] and de Bruijn graphs =-=[18, 12, 25, 1, 20]. -=-Randomized P2P networks include Viceroy [21] (a randomized emulation of butterfly networks), Symphony [23] (an adaptation of Kleinberg’s construction [19]), randomized-hypercubes [15, 8], randomized... |

45 | Routing networks for distributed hash tables
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(Show Context)
Citation Context ...tworks), Symphony [23] (an adaptation of Kleinberg’s construction [19]), randomized-hypercubes [15, 8], randomizedChord [36, 15], and a combination of Kleinberg’s construction with butterfly netwo=-=rks [22].-=- The tradeoff between the average path length and the outdegree of nodes, is of fundamental interest to designers of P2P routing networks. Hypercubes and Chord offer average paths of length Θ(log n) ... |

41 | Incrementally Improving Lookup Latency in Distributed Hash Table Systems
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(Show Context)
Citation Context ...n k ) both by Manku et al [23] and by Aspnes et al [3]. Recently, three more randomized P2P networks have been devised, all of which use greedy routing: randomized-hypercube [15, 8], randomized-Chord =-=[15, 36],-=- and skip-graphs [4] (also known as SkipNet [17]). Randomized-Chord is a variation on a deterministic P2P routing network called Chord [34, 14]. Skip1 According to Barabási [5] this idea may have its... |

32 | Optimal routing in chord
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(Show Context)
Citation Context ...routing: randomized-hypercube [15, 8], randomized-Chord [15, 36], and skip-graphs [4] (also known as SkipNet [17]). Randomized-Chord is a variation on a deterministic P2P routing network called Chord =-=[34, 14]. Ski-=-p1 According to Barabási [5] this idea may have its origins in a short story “Chains” by the Hungarian writer Frigyes Karinthy from 1929; this idea has been retold and recast many times since the... |

20 | Know Thy Neighbor’s Neighbor: Better Routing for
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(Show Context)
Citation Context ...2P network that supports prefix search. Simulations show that for network sizes ranging from 2 12 to 2 24 nodes, NoN-greedy routes are 40% to 48% shorter than greedy routes in all of these topologies =-=[23, 26]. -=-Lower bounds We show that greedy routing requires Ω(log n) hops on average in each of the following randomized P2P networks: skip-graphs, randomized-Chord, randomizedhypercube, and Symphony with k =... |

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Citation Context ...n edge exists between a pair of nodes with some positive probability. The question of existence of infinite components was considered by Schulman [33], Aizenman and Newman [2] and Newman and Schulman =-=[27], where -=-the one dimensional lattice Z is studied and edges (i, j) are selected with probability β/�i − j� s for some values β, s. Benjamini and Berger [7] proposed and studied a finite percolation mod... |

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Citation Context ...colation”. In that model, nodes lie on a lattice and an edge exists between a pair of nodes with some positive probability. The question of existence of infinite components was considered by Schulma=-=n [33], Aizenm-=-an and Newman [2] and Newman and Schulman [27], where the one dimensional lattice Z is studied and edges (i, j) are selected with probability β/�i − j� s for some values β, s. Benjamini and Be... |

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Citation Context ...nodes lie on a lattice and an edge exists between a pair of nodes with some positive probability. The question of existence of infinite components was considered by Schulman [33], Aizenman and Newman =-=[2] and New-=-man and Schulman [27], where the one dimensional lattice Z is studied and edges (i, j) are selected with probability β/�i − j� s for some values β, s. Benjamini and Berger [7] proposed and stu... |

6 |
brief announcement) An overview of the content-addressable network D2B
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(Show Context)
Citation Context |

6 | Eclecticism shrinks the world
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(Show Context)
Citation Context ...log n is O( ) w.h.p. NoN-greedy routing was first used log log n (under the name “greedy with 1-lookahead”) by Manku et al [23] as a heuristic for Symphony, a randomized P2Psnetwork. Fraigniaud et=-= al [13] r-=-ecently analyzed greedy algorithms in Kleinberg’s model, when each node is aware of the long-range contacts of the log n nodes which are closest to it. They show that a variant of NoN-greedy routes ... |

3 | Brief Announcement: Deterministic SkipNet
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- 2003
(Show Context)
Citation Context ...ly considered as a negative by-product and much effort is put in reducing it. For instance, a deterministic P2P routing network that guarantees that the skip graph is almost ‘perfect’ is presented=-= in [16]. -=-As was noticed by Harvey et al [17], a perfect skip graph is similar to Chord [34]. The average length of shortest paths in both Chord (studied in [14]) and hypercubes is Ω(log n). This leads to the... |

1 |
The diameter of a longe-range percolation clusters on finite cycles. Random Structures and Algorithms
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(Show Context)
Citation Context ...enman and Newman [2] and Newman and Schulman [27], where the one dimensional lattice Z is studied and edges (i, j) are selected with probability β/�i − j� s for some values β, s. Benjamini and=-= Berger [7] proposed a-=-nd studied a finite percolation model: a cycle graph over n nodes where an edge between nodes i and j exists with probability 1 if �i−j� = 1, otherwise, it exists with probability exp(−β/�i... |

1 |
The diameter of a longe-range percolation graph. Random Structures and Algorithms
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(Show Context)
Citation Context ...e hope that our results inspire further investigations into the general properties of these networks. The basic idea of the NoN-greedy approach is drawn from two sources. A paper by Coppersmith et al =-=[10]-=- uses the neighbors-of-neighbors approach, though not in an algorithmic perspective. They use the idea to establish that the diameter of small-world percolation networks on n nodes log n is O( ) w.h.p... |