### Abstract

We consider the problem of name-independent routing in doubling metrics. A doubling metric is a metric space whose doubling dimension is a constant, where the doubling dimension of a metric space is the least value α such that any ball of radius r can be covered by at most 2^{α} balls of radius r/2. Given any δ > 0 and a weighted undirected network G whose shortest path metric d is a doubling metric with doubling dimension α, we present a name-independent routing scheme for G with (9+δ)-stretch, (2+ 1/δ)^{O(α)}(log Δ)^{2}(log n)-bit routing information at each node, and packet headers of size O(log n), where Δ is the ratio of the largest to the smallest shortest path distance in G. In addition, we prove that for any ε ∈. (0, 8), there is a doubling metric network G with n nodes, doubling dimension α ≤ 6 - log ε, and Δ = O(2^{1/ε}n) such that any name-independent routing scheme on G with routing information at each node of size o(n ^{(ε60)2})-bits has stretch larger than 9 - ε. Therefore assuming that Δ is bounded by a polynomial on n, our algorithm basically achieves optimal stretch for name-independent routing in doubling metrics with packet header size and routing information at each node both bounded by a polylogarithmic function of n.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |

Pages | 198-207 |

Number of pages | 10 |

Volume | 2006 |

State | Published - 2006 |

Event | 25th Annual ACM Symposium on Principles of Distributed Computing 2006 - Denver, CO, United States Duration: Jul 23 2006 → Jul 26 2006 |

### Other

Other | 25th Annual ACM Symposium on Principles of Distributed Computing 2006 |
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Country | United States |

City | Denver, CO |

Period | 7/23/06 → 7/26/06 |

### Fingerprint

### Keywords

- Compact Routing
- Doubling Metrics
- Name-Independent Routing

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture

### Cite this

*Proceedings of the Annual ACM Symposium on Principles of Distributed Computing*(Vol. 2006, pp. 198-207)

**Optimal-stretch name-independent compact routing in doubling metrics.** / Konjevod, Goran; Richa, Andrea; Xia, Donglin.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual ACM Symposium on Principles of Distributed Computing.*vol. 2006, pp. 198-207, 25th Annual ACM Symposium on Principles of Distributed Computing 2006, Denver, CO, United States, 7/23/06.

}

TY - GEN

T1 - Optimal-stretch name-independent compact routing in doubling metrics

AU - Konjevod, Goran

AU - Richa, Andrea

AU - Xia, Donglin

PY - 2006

Y1 - 2006

N2 - We consider the problem of name-independent routing in doubling metrics. A doubling metric is a metric space whose doubling dimension is a constant, where the doubling dimension of a metric space is the least value α such that any ball of radius r can be covered by at most 2α balls of radius r/2. Given any δ > 0 and a weighted undirected network G whose shortest path metric d is a doubling metric with doubling dimension α, we present a name-independent routing scheme for G with (9+δ)-stretch, (2+ 1/δ)O(α)(log Δ)2(log n)-bit routing information at each node, and packet headers of size O(log n), where Δ is the ratio of the largest to the smallest shortest path distance in G. In addition, we prove that for any ε ∈. (0, 8), there is a doubling metric network G with n nodes, doubling dimension α ≤ 6 - log ε, and Δ = O(21/εn) such that any name-independent routing scheme on G with routing information at each node of size o(n (ε60)2)-bits has stretch larger than 9 - ε. Therefore assuming that Δ is bounded by a polynomial on n, our algorithm basically achieves optimal stretch for name-independent routing in doubling metrics with packet header size and routing information at each node both bounded by a polylogarithmic function of n.

AB - We consider the problem of name-independent routing in doubling metrics. A doubling metric is a metric space whose doubling dimension is a constant, where the doubling dimension of a metric space is the least value α such that any ball of radius r can be covered by at most 2α balls of radius r/2. Given any δ > 0 and a weighted undirected network G whose shortest path metric d is a doubling metric with doubling dimension α, we present a name-independent routing scheme for G with (9+δ)-stretch, (2+ 1/δ)O(α)(log Δ)2(log n)-bit routing information at each node, and packet headers of size O(log n), where Δ is the ratio of the largest to the smallest shortest path distance in G. In addition, we prove that for any ε ∈. (0, 8), there is a doubling metric network G with n nodes, doubling dimension α ≤ 6 - log ε, and Δ = O(21/εn) such that any name-independent routing scheme on G with routing information at each node of size o(n (ε60)2)-bits has stretch larger than 9 - ε. Therefore assuming that Δ is bounded by a polynomial on n, our algorithm basically achieves optimal stretch for name-independent routing in doubling metrics with packet header size and routing information at each node both bounded by a polylogarithmic function of n.

KW - Compact Routing

KW - Doubling Metrics

KW - Name-Independent Routing

UR - http://www.scopus.com/inward/record.url?scp=33748678507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748678507&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33748678507

SN - 1595933840

SN - 9781595933843

VL - 2006

SP - 198

EP - 207

BT - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

ER -