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Online and dynamic embeddings of approximate ultrametrics

Published: 18 August 2008 Publication History

Abstract

In many network applications it would be useful for individual nodes to have knowledge of distances (e.g. latency or bandwidth) in the network. If every node stored all distances then it would take Ω(n2) space at every node, and furthermore when a new node joins it would have to send an Ω(n)-bit message to Ω(n) other nodes, for a total communication complexity of Ω(n2) per update. In this paper we consider a specific class of metrics, those obeying an ε-three point condition, and show that by embedding these metrics into ultrametrics we can use only O(n) space at every node, have amortized communication complexity of O(n4/3) (allowing nodes to join and leave the network), and still estimate distances up to a (1+ε)log n + 5-stretch factor.

References

[1]
I. Abraham, M. Balakrishnan, F. Kuhn, D. Malkhi, V. Ramasubramanian, and K. Talwar. Reconstructing approximate tree metrics. In PODC '07: Proceedings of the twenty-sixth annual ACM Symposium on Principles of Distributed Computing, pages 43--52, New York, NY, USA, 2007. ACM.
[2]
F. Dabek, R. Cox, F. Kaashoek, and R. Morris. Vivaldi: a decentralized network coordinate system. SIGCOMM Comput. Commun. Rev., 34(4):15--26, 2004.

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cover image ACM Conferences
PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
August 2008
474 pages
ISBN:9781595939890
DOI:10.1145/1400751
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 18 August 2008

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Author Tags

  1. dynamic
  2. embeddings
  3. metric spaces
  4. online
  5. ultrametrics

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  • Demonstration

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PODC '08

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Overall Acceptance Rate 740 of 2,477 submissions, 30%

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