## Compact Routing with Minimum Stretch (0)

Venue: | Journal of Algorithms |

Citations: | 111 - 5 self |

### BibTeX

@ARTICLE{Cowen_compactrouting,

author = {Lenore Cowen},

title = {Compact Routing with Minimum Stretch},

journal = {Journal of Algorithms},

year = {},

volume = {38},

pages = {255--260}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all nodes in an arbitrary weighted undirected network. This answers an open question of Gavoille and Gengler who showed that any universal compact routing algorithm with maximum stretch strictly less than 3 must use\Omega\Gamma n) local space at some vertex. 1 Introduction Let G = (V; E) with jV j = n be a labeled undirected network. Assuming that a positive cost, or distance is assigned with each edge, the stretch of path p(u; v) from node u to node v is defined as jp(u;v)j jd(u;v)j , where jd(u; v)j is the length of the shortest u \Gamma v path. The approximate all-pairs shortest path problem involves a tradeoff of stretch against time-- short paths with stretch bounded by a constant are com...

### Citations

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Citation Context ...ensity dependent notion of near and far distances in order to achieve its bounds, as described in Section 4. 3 Preliminaries The algorithm uses the following known theorem for landmark selection (see =-=[4, 16]-=-). Theorem 3.1. (Extended dominating set) Let G = (V; E) be a weighted undirected graph. Let B v denote the set of v's n ff closest neighbors (where ties are broken lexicographically according to orig... |

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Citation Context ...ra with source l For each u 2 V Store (l; e u (l)) at u Figure 2: The storage algorithm rithm) resemble the approximate shortest path algorithms of [10]. In fact, we are constructing a 3-spanner (see =-=[3, 10, 17]-=-). However, we are doing more work than the best tradeoffs achieved by those other algorithms, because our goal is not only to produce approximate shortest paths, but to have small local space. Thus w... |

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Citation Context ...ra with source l For each u 2 V Store (l; e u (l)) at u Figure 2: The storage algorithm rithm) resemble the approximate shortest path algorithms of [10]. In fact, we are constructing a 3-spanner (see =-=[3, 10, 17]-=-). However, we are doing more work than the best tradeoffs achieved by those other algorithms, because our goal is not only to produce approximate shortest paths, but to have small local space. Thus w... |

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Citation Context ... some node for any routing scheme with stretch strictly less than 3. Previous work. Early work on the compact routing problem focused on routing schemes for special case networks such as rings, trees =-=[20]-=-, complete networks and grids [21, 22]. Fredrickson and Janardan [12, 13] considered compact routing in networks with small separators, such as outerplanar networks, and also derived small stretch alg... |

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Citation Context ...t path problem involves a tradeoff of stretch against time-- short paths with stretch bounded by a constant are computed in time less than it would take to compute exact all-pairs shortest paths (see =-=[1, 2, 6, 8, 9, 10]-=-). The compact routing problem considers instead a tradeoff of stretch for space, in the setting where each node locally stores its own routing tables. The stretch of a compact routing algorithm is de... |

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Citation Context ...t path problem involves a tradeoff of stretch against time-- short paths with stretch bounded by a constant are computed in time less than it would take to compute exact all-pairs shortest paths (see =-=[1, 2, 6, 8, 9, 10]-=-). The compact routing problem considers instead a tradeoff of stretch for space, in the setting where each node locally stores its own routing tables. The stretch of a compact routing algorithm is de... |

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Citation Context ...than maximum space at each node. An algorithm of [5] achieves the optimum of stretch 3 and O(n 3=2 log n) space total, but some individual nodes use O(n log n) space in this scheme. Further work (see =-=[4]-=-) argued successfully that it was most important to bound the maximum space, and this has been the focus of recent work. The best bounds on maximum local space were achieved for different ranges of st... |

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Citation Context ...Previous work. Early work on the compact routing problem focused on routing schemes for special case networks such as rings, trees [20], complete networks and grids [21, 22]. Fredrickson and Janardan =-=[12, 13]-=- considered compact routing in networks with small separators, such as outerplanar networks, and also derived small stretch algorithms for compact routing in planar networks. Peleg and Upfal [18, 19] ... |

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Citation Context ...ing schemes that worked on all undirected networks. Some of the earlier work on this problem presented schemes that bounded only average space, rather than maximum space at each node. An algorithm of =-=[5]-=- achieves the optimum of stretch 3 and O(n 3=2 log n) space total, but some individual nodes use O(n log n) space in this scheme. Further work (see [4]) argued successfully that it was most important ... |

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Citation Context ...with stretch strictly less than 3. Previous work. Early work on the compact routing problem focused on routing schemes for special case networks such as rings, trees [20], complete networks and grids =-=[21, 22]-=-. Fredrickson and Janardan [12, 13] considered compact routing in networks with small separators, such as outerplanar networks, and also derived small stretch algorithms for compact routing in planar ... |

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Citation Context ...t path problem involves a tradeoff of stretch against time-- short paths with stretch bounded by a constant are computed in time less than it would take to compute exact all-pairs shortest paths (see =-=[1, 2, 6, 8, 9, 10]-=-). The compact routing problem considers instead a tradeoff of stretch for space, in the setting where each node locally stores its own routing tables. The stretch of a compact routing algorithm is de... |

63 | Space-efficiency for routing schemes of stretch factor three
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Citation Context ...-96-1-0829. Author's email: cowen@cs.jhu.edu at each node? It does so by presenting the first such algorithm with stretch 3. The matching lower bound comes from a recent paper of Gavoille and Gengler =-=[15]-=- who proved that there exists an n-node network that requires\Omega\Gamma n) space at some node for any routing scheme with stretch strictly less than 3. Previous work. Early work on the compact routi... |

61 | Compact routing schemes with low stretch factor
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Citation Context ...to bound the maximum space, and this has been the focus of recent work. The best bounds on maximum local space were achieved for different ranges of stretch by different papers: A recent algorithm of =-=[11]-=- achieves O(n 1=2 log n) maximum local space with maximum stretch bounded by 5; the paper of [7] give tradeoffs of stretch versus space that result in sublinear local space when the maximum stretch is... |

42 |
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Citation Context ...Previous work. Early work on the compact routing problem focused on routing schemes for special case networks such as rings, trees [20], complete networks and grids [21, 22]. Fredrickson and Janardan =-=[12, 13]-=- considered compact routing in networks with small separators, such as outerplanar networks, and also derived small stretch algorithms for compact routing in planar networks. Peleg and Upfal [18, 19] ... |

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Citation Context |

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Citation Context ... [12, 13] considered compact routing in networks with small separators, such as outerplanar networks, and also derived small stretch algorithms for compact routing in planar networks. Peleg and Upfal =-=[18, 19]-=- were the first to construct universal compact routing schemes, that is, compact routing schemes that worked on all undirected networks. Some of the earlier work on this problem presented schemes that... |

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Citation Context |

18 |
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(Show Context)
Citation Context ...with stretch strictly less than 3. Previous work. Early work on the compact routing problem focused on routing schemes for special case networks such as rings, trees [20], complete networks and grids =-=[21, 22]-=-. Fredrickson and Janardan [12, 13] considered compact routing in networks with small separators, such as outerplanar networks, and also derived small stretch algorithms for compact routing in planar ... |

14 |
Routing with polynomial communication space tradeoff
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(Show Context)
Citation Context ...m local space were achieved for different ranges of stretch by different papers: A recent algorithm of [11] achieves O(n 1=2 log n) maximum local space with maximum stretch bounded by 5; the paper of =-=[7]-=- give tradeoffs of stretch versus space that result in sublinear local space when the maximum stretch iss16, and beat the space requirements of [11] for maximum stretch ? 64. No algorithm which beat t... |

2 |
A survey on interval routing scheme. Technical Memo RR-1182-97, Laboratoire Bordelais de Recherche en Informatique
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(Show Context)
Citation Context ...ents we present are at the algorithmic, not at the protocol level, and go through in the same distributed model with no additional complication. The reader is also referred to the excellent survey of =-=[14]-=-. For those unfamiliar with past work in the area, however, it is worth making a remark, about node-names and output edge-names, both of which are implementation issues common to all papers in the are... |