## Fault-tolerant Routing in Peer-to-peer Systems (2003)

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Citations: | 64 - 1 self |

### BibTeX

@MISC{Aspnes03fault-tolerantrouting,

author = {James Aspnes and Zoë Diamadi and Gauri Shah},

title = {Fault-tolerant Routing in Peer-to-peer Systems},

year = {2003}

}

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### Abstract

We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system. We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points represent resource identifiers, where the probability of a connection between two nodes depends only on the distance between them in the metric space. We study the performance of a peer-to-peer system where nodes are embedded at grid points in a simple metric space: a one-dimensional real line. We prove upper and lower bounds on the message complexity of locating particular resources in such a system, under a variety of assumptions about failures of either nodes or the connections between them. Our lower bounds in particular show that the use of inverse power-law distributions in routing, as suggested by Kleinberg [5], is close to optimal. We also give efficient heuristics to dynamically maintain such a system as new nodes arrive and old nodes depart. Finally, we give experimental results that suggest promising directions for future work.

### Citations

3847 | Chord: A scalable peer-to-peer lookup service for internet applications
- Stoica, Morris, et al.
- 2001
(Show Context)
Citation Context ...es the problem somewhat in practice, it does not improve performance in the limit. Some of these first-generation systems have inspired the development of more sophisticated ones like CAN [11], Chord =-=[13]-=- and Tapestry [2]. CAN partitions a d-dimensional metric space into zones. Each key is mapped to a point in some zone and stored at the node that owns the zone. Each node stores O(d) information, and ... |

2957 | A scalable content-addressable network
- Ratnasamy, Francis, et al.
- 2001
(Show Context)
Citation Context ...7] ameliorates the problem somewhat in practice, it does not improve performance in the limit. Some of these first-generation systems have inspired the development of more sophisticated ones like CAN =-=[11]-=-, Chord [13] and Tapestry [2]. CAN partitions a d-dimensional metric space into zones. Each key is mapped to a point in some zone and stored at the node that owns the zone. Each node stores O(d) infor... |

514 | Accessing nearby copies of replicated objects in a distributed environment
- Plaxton, Rajaraman, et al.
- 1997
(Show Context)
Citation Context ... is done greedily to the farthest possible node in the routing table, and it is not hard to see that this gives an O(log n) delivery time with n nodes in the system. Tapestry uses Plaxton’s algorithm =-=[10]-=-, a form of suffix-based, hypercube routing, as the routing mechanism: in this algorithm, the message is forwarded deterministically to a node whose identifier is one digit closer to the target identi... |

217 |
A scheme for fast parallel communication
- Valiant
- 1982
(Show Context)
Citation Context ...y choose another node, deliver the message to this new node and then try to deliver the message from this node to the original destination node (similar to the hypercube routing strategy explained in =-=[14]-=-). 26sProbability of link 0.1 0.01 0.001 0.0001 1e-05 DERIVED IDEAL 1e-06 1 10 100 1000 10000 100000 Length of link (a) The derived distribution. Absolute error 0.005 0 -0.005 -0.01 -0.015 -0.02 DERIV... |

148 | Small-World Phenomena and the Dynamics of Information
- Kleinberg
(Show Context)
Citation Context ....3. Suppose that there are ℓ links from each node. We consider different strategies for generating links and routing depending on number of links ℓ in two ranges: ℓ ∈ [1,lg n] and ℓ ∈ (lg n,n c ]. In =-=[6]-=-, Kleinberg uses a group structure to get a delivery time of O(log n) for the case of a polylogarithmic number of links. However, he uses a more complicated algorithm for routing while we obtain the s... |

146 | Spatial gossip and resource location protocols
- Kempe, Kleinberg, et al.
- 2001
(Show Context)
Citation Context ... the nodes in real space; good network-building and search mechanisms for this model might allow efficient location of nearby instances of a resource without having to resort to local flooding (as in =-=[4]-=-). Another promising direction would be to study the security properties of greedy routing schemes to see how they can be adapted to provide desirable properties like anonymity or robustness against B... |

116 | Building low-diameter P2P networks
- Pandurangan, Raghavan, et al.
- 2001
(Show Context)
Citation Context ...y described previously. We omit those results because it is difficult to distinguish between the results of the two strategies on the scale used for our graphs. There has also been other related work =-=[9]-=- on how to construct, with the support of a central server, random graphs with many desirable properties, such as small diameter and guaranteed connectivity with high probability. Although it is not c... |

87 | Using the Small World Model to Improve Freenet Performance
- Goel, Govindan
(Show Context)
Citation Context ...ng links to be replaced by a link to v. The choice of the link to replace can vary. We use a strategy that builds on the work of Sarshar et al.[12]. In that work, the authors use ideas of Zhang et al.=-=[15]-=- to build a graph where each node has a single long-distance link to a node at distance d with probability 1/d. When a node with a long-distance link at distance d1 encounters a new node at distance d... |

22 |
The complexity of parallel search
- Karp, Upfal, et al.
- 1988
(Show Context)
Citation Context ...number of failures. 4. ROUTING In this section, we present our lower and upper bounds on greedy routing. 4.1 Tools Some of our upper bounds will be proved using a well-known upper bound of Karp et al.=-=[3]-=- on probabilistic recurrence relations. We will restate this bound as Lemma 1, and then show how a similar technique can be used to get lower bounds with some additional conditions in Theorem 2. Lemma... |

11 | Chord: A scalable peer-to -peer lookup service for internet applications - Stoica, Morris, et al. |

6 |
Tapestry: An infrastructure for fault-tolerant wide-area location and routing
- Joseph, Kubiatowicz, et al.
- 2001
(Show Context)
Citation Context ...ewhat in practice, it does not improve performance in the limit. Some of these first-generation systems have inspired the development of more sophisticated ones like CAN [11], Chord [13] and Tapestry =-=[2]-=-. CAN partitions a d-dimensional metric space into zones. Each key is mapped to a point in some zone and stored at the node that owns the zone. Each node stores O(d) information, and resource location... |

5 |
The small-world phenomenon:an algorithmic perspective
- Kleinberg
- 2000
(Show Context)
Citation Context ...f assumptions about failures of either nodes or the connections between them. Our lower bounds in particular show that the use of inverse power-law distributions in routing, as suggested by Kleinberg =-=[5]-=-, is close to optimal. We also give efficient heuristics to dynamically maintain such a system as new nodes arrive and old nodes depart. Finally, we give experimental results that suggest promising di... |

3 | A random structure for optimum cache size distributed hash table (DHT) peer-to-peer design
- Sarshar, Roychowdhury
- 2002
(Show Context)
Citation Context ...t u responds to v’s request by choosing one of its existing links to be replaced by a link to v. The choice of the link to replace can vary. We use a strategy that builds on the work of Sarshar et al.=-=[12]-=-. In that work, the authors use ideas of Zhang et al.[15] to build a graph where each node has a single long-distance link to a node at distance d with probability 1/d. When a node with a long-distanc... |

3 |
Building low-diameter P2P networks
- Panduragan, Raghavan, et al.
- 2001
(Show Context)
Citation Context ...y described previously. We omit those results because it is difficult to distinguish between the results of the two strategies on the scale used for our graphs. There has also been other related work =-=[9]-=- on how to construct, with the support of a central server, random graphs with many desirable properties, such as small diameter and guaranteed connectivity with high probability. Although it is not c... |

1 |
The complexity of parallel search. Journal of Computer and System Sciences, 36(2):225–253
- Karp, Upfal, et al.
- 1988
(Show Context)
Citation Context ...wer-law distribution with exponent 1 and analyze the effects on performance in the presence of failures. 4.1 Tools Some of our upper bounds will be proved using a well-known upper bound of Karp et al.=-=[3]-=- on probabilistic recurrence relations. We will restate this bound as Lemma 1, and then show how a similar technique can be used to get lower bounds with some additional conditions in Theorem 2. Lemma... |