## Compact roundtrip routing with topology-independent node names (2003)

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Venue: | In Proceedings of the Twenty-Second Annual Symposium on Principles of Distributed Computing |

Citations: | 7 - 0 self |

### BibTeX

@INPROCEEDINGS{Arias03compactroundtrip,

author = {Marta Arias and Lenore J. Cowen and Kofi A. Laing},

title = {Compact roundtrip routing with topology-independent node names},

booktitle = {In Proceedings of the Twenty-Second Annual Symposium on Principles of Distributed Computing},

year = {2003},

pages = {43--52},

publisher = {ACM Press}

}

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### Abstract

This paper presents compact roundtrip routing schemes with local tables of size Õ( √ n) and stretch 6 for any directed network with arbitrary edge weights; and with local tables of size Õ(ǫ−1 n 2/k) and stretch min((2 k/2 − 1)(k + ǫ),16k 2 + 8k − 8), for any directed network with polynomially-sized edges, both in the topology-independent node-name model. 1 These are the first topology-independent results that apply to routing in directed networks.

### Citations

3855 | Chord: A scalable peer-to-peer lookup service for internet applications
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(Show Context)
Citation Context ...nds can be tightened. In the undirected TINN case, the known upper and lower bounds are 5 and 3 (see [1] and [12] respectively). Finally, peer to peer networks has been a topic of increasing interest =-=[13, 16, 19, 21, 23, 24, 28, 29]-=-. It has been suggested to us [7, 20] that some of the techniques developed here, could perhaps be applied to the design of better algorithms for routing and searching in peer-to-peer networks. 7. REF... |

2964 | A scalable content-addressable network
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- 2001
(Show Context)
Citation Context ...nds can be tightened. In the undirected TINN case, the known upper and lower bounds are 5 and 3 (see [1] and [12] respectively). Finally, peer to peer networks has been a topic of increasing interest =-=[13, 16, 19, 21, 23, 24, 28, 29]-=-. It has been suggested to us [7, 20] that some of the techniques developed here, could perhaps be applied to the design of better algorithms for routing and searching in peer-to-peer networks. 7. REF... |

1856 | Pastry: Scalable, distributed object location and routing for large-scale peer-to-peer systems
- Rowstron, Druschel
- 2001
(Show Context)
Citation Context ...nds can be tightened. In the undirected TINN case, the known upper and lower bounds are 5 and 3 (see [1] and [12] respectively). Finally, peer to peer networks has been a topic of increasing interest =-=[13, 16, 19, 21, 23, 24, 28, 29]-=-. It has been suggested to us [7, 20] that some of the techniques developed here, could perhaps be applied to the design of better algorithms for routing and searching in peer-to-peer networks. 7. REF... |

1374 |
Introduction to Parallel Algorithms and Architectures: Arrays
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Citation Context ...he outbound phase. Algorithm 3.4 is presented below. The idea of matching increasing prefixes of node names is well known in the parallel algorithms literature for multidimensional array routing (see =-=[17]-=-); it has also been used more recently in the context of peer to peer systems for locating replicated objects [26, 16, 19, 13], and also for compact routing in undirected graphs [1]. Algorithm 3.4. fo... |

1131 | Tapestry: An infrastructure for fault-tolerant wide-area location and routing
- Zhao, Kubiatowicz, et al.
- 2001
(Show Context)
Citation Context |

1006 | OceanStore: An Architecture for Global-Scale Persistent Storage
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Citation Context ...l known in the parallel algorithms literature for multidimensional array routing (see [17]); it has also been used more recently in the context of peer to peer systems for locating replicated objects =-=[26, 16, 19, 13]-=-, and also for compact routing in undirected graphs [1]. Algorithm 3.4. for i ← 0 upto k − 1 step 1: if (i+1 < k): vi+1 ← closest node to vi in the set N i+1 (vi) T {v|∃Bβ ∈ Sv : σ i+1 (Bβ) = σ i+1 (〈... |

517 | Accessing nearby copies of replicated objects in a distributed environment
- Plaxton, Rajaraman, et al.
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(Show Context)
Citation Context ...l known in the parallel algorithms literature for multidimensional array routing (see [17]); it has also been used more recently in the context of peer to peer systems for locating replicated objects =-=[26, 16, 19, 13]-=-, and also for compact routing in undirected graphs [1]. Algorithm 3.4. for i ← 0 upto k − 1 step 1: if (i+1 < k): vi+1 ← closest node to vi in the set N i+1 (vi) T {v|∃Bβ ∈ Sv : σ i+1 (Bβ) = σ i+1 (〈... |

201 | Compact routing schemes
- Thorup, Zwick
- 2001
(Show Context)
Citation Context ...ependent node-name model first introduced by Awerbuch and Peleg in 1989. Most recent results in compact routing (and all previous results on compact roundtrip routing in directed networks) (see, e.g. =-=[4, 6, 9, 10, 14, 15, 22, 25]-=- and the surveys of [11, 30]) have been in a model where the routing scheme designer may assign his/her own O(log n)-bit or sometimes O(log 2 n)-bit node labels, dependent on network topology. That is... |

185 | Distributed Object Location in a Dynamic Network
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- 2002
(Show Context)
Citation Context ...l known in the parallel algorithms literature for multidimensional array routing (see [17]); it has also been used more recently in the context of peer to peer systems for locating replicated objects =-=[26, 16, 19, 13]-=-, and also for compact routing in undirected graphs [1]. Algorithm 3.4. for i ← 0 upto k − 1 step 1: if (i+1 < k): vi+1 ← closest node to vi in the set N i+1 (vi) T {v|∃Bβ ∈ Sv : σ i+1 (Bβ) = σ i+1 (〈... |

137 |
Sparse partitions
- Awerbuch, Peleg
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(Show Context)
Citation Context ...) Awerbuch et al., in the same paper where they introduced the TINN model, produced the first TINN compact routing schemes for undirected networks. A paper of Awerbuch and Peleg in the following year =-=[3]-=-, presented an alternate scheme with a polynomial space/stretch tradeoff. Our recent result joint with Rajaraman and Taka [1], presents compactrouting TINN schemes that achieve a reduction in the maxi... |

112 | Compact routing with minimum stretch - Cowen |

88 | Routing in trees
- Fraigniaud, Gavoille
- 2001
(Show Context)
Citation Context ...ependent node-name model first introduced by Awerbuch and Peleg in 1989. Most recent results in compact routing (and all previous results on compact roundtrip routing in directed networks) (see, e.g. =-=[4, 6, 9, 10, 14, 15, 22, 25]-=- and the surveys of [11, 30]) have been in a model where the routing scheme designer may assign his/her own O(log n)-bit or sometimes O(log 2 n)-bit node labels, dependent on network topology. That is... |

83 | All Pairs Almost Shortest Paths
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- 2000
(Show Context)
Citation Context ...cting (one-way, topology-dependent) compact routing schemes on directed networks; and it appears that it is hard to “compact” routing schemes when the network is directed. For example, it is shown in =-=[8]-=- that distinguishing between pairs of vertices at distances 2 and ∞ even in unweighted directed graphs is at least as hard as Boolean matrix multiplication. Rodittyset al. [22] observe that sparse spa... |

81 | Brocade: Landmark routing on overlay networks
- Zhao, Duan, et al.
- 2002
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Citation Context |

73 | Compact distributed data structures for adaptive routing - Awerbuch, Bar-Noy, et al. - 1989 |

64 | Space–efficiency of routing schemes of stretch factor three
- Gavoille, Gengler
(Show Context)
Citation Context ...he abstract. Finally, some work has been done on lower bounds for (one-way) compact routing in undirected graphs, that applies to the TINN model. In particular, a construction of Gavoille and Gengler =-=[12]-=- implies that any compact routPSfrag replacements ing scheme that uses o(n)-sized tables at every node in the TINN model, must have stretch ≥ 3. (In fact, the result of [12] is stronger; the lower bou... |

62 | Compact routing schemes with low stretch factor
- Eilam, Gavoille, et al.
- 1998
(Show Context)
Citation Context ...ependent node-name model first introduced by Awerbuch and Peleg in 1989. Most recent results in compact routing (and all previous results on compact roundtrip routing in directed networks) (see, e.g. =-=[4, 6, 9, 10, 14, 15, 22, 25]-=- and the surveys of [11, 30]) have been in a model where the routing scheme designer may assign his/her own O(log n)-bit or sometimes O(log 2 n)-bit node labels, dependent on network topology. That is... |

60 | Exact and approximate distances in graphs - a survey
- Zwick
- 2001
(Show Context)
Citation Context ...buch and Peleg in 1989. Most recent results in compact routing (and all previous results on compact roundtrip routing in directed networks) (see, e.g. [4, 6, 9, 10, 14, 15, 22, 25] and the surveys of =-=[11, 30]-=-) have been in a model where the routing scheme designer may assign his/her own O(log n)-bit or sometimes O(log 2 n)-bit node labels, dependent on network topology. That is, when a packet ∗ Supported ... |

51 | Routing in distributed networks: overview and open problems
- Gavoille
(Show Context)
Citation Context ...buch and Peleg in 1989. Most recent results in compact routing (and all previous results on compact roundtrip routing in directed networks) (see, e.g. [4, 6, 9, 10, 14, 15, 22, 25] and the surveys of =-=[11, 30]-=-) have been in a model where the routing scheme designer may assign his/her own O(log n)-bit or sometimes O(log 2 n)-bit node labels, dependent on network topology. That is, when a packet ∗ Supported ... |

40 | A.S.: A Model for Worldwide Tracking of Distributed Objects
- Steen, Hauck, et al.
- 1996
(Show Context)
Citation Context |

33 |
Compact roundtrip routing in directed networks
- Cowen, Wagner
(Show Context)
Citation Context |

33 | Roundtrip spanners and roundtrip routing in directed graphs
- Roditty, Thorup, et al.
- 2002
(Show Context)
Citation Context |

29 | Compact routing with name independence
- Arias, Cowen, et al.
- 2003
(Show Context)
Citation Context ...r undirected networks. A paper of Awerbuch and Peleg in the following year [3], presented an alternate scheme with a polynomial space/stretch tradeoff. Our recent result joint with Rajaraman and Taka =-=[1]-=-, presents compactrouting TINN schemes that achieve a reduction in the maximum length of the routes or stretch of these schemes. These schemes, like the ones we present in this paper, are universal, m... |

22 |
Distance-dependent distributed directories
- Peleg
- 1993
(Show Context)
Citation Context ...we will write up to O(log 2 n) bits of learned routing information into the packet header. 1.2 Our Results A key idea in all our schemes is that of a distributed dictionary, first introduced by Peleg =-=[18]-=-. In each of our schemes, we assign blocks of dictionary entries to nodes in a balanced way, while ensuring that the entire address space is covered in some neighborhood structure (or recursive neighb... |

7 |
Compact routing with stretch factor of less than three
- Iwama, Kawachi
- 2000
(Show Context)
Citation Context |

5 | Compact roundtrip routing for digraphs
- Cowen, Wagner
- 1999
(Show Context)
Citation Context ...ck. 2. STRETCH 6 SCHEME In this section, we construct a TINN compact roundtrip routing scheme with Õ(n1/2 )-sized routing tables, O(log 2 n)sized routing headers, while achieving stretch 6. Following =-=[5]-=- and [22], we define the roundtrip distance metric as follows: let G = (V, E) be an edge-weighted directed graph. Recall that d(u, v) denotes the shortest path from u to v, and r(u, v) = d(u, v)+d(v, ... |

2 |
Compact routing for average case networks
- Iwama, Okita
- 2002
(Show Context)
Citation Context |

2 |
Drawing with Bezier Curves and Routing on Digraphs
- Wagner
- 1999
(Show Context)
Citation Context ...n in unweighted directed graphs is at least as hard as Boolean matrix multiplication. Rodittyset al. [22] observe that sparse spanners don’t exist for all digraphs, and there is further discussion in =-=[6, 27]-=-. In the 2000 PODC conference, Cowen and Wagner [6] made the observation that in directed graphs, instead of bounding the length of a one-way path from node x to node y in terms of the shortest distan... |