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On the complexity of greedy routing in ring-based peer-to-peer networks

Published: 12 August 2007 Publication History

Abstract

We investigate the complexity of greedy routing in uniform ring-based random graphs, a general model that captures many topologies that have been proposed for peer-to-peer and social networks. In this model the nodes form a ring; for each node u we independently draw the set of distances along the ring from u to its "long-range contacts" from a fixed distribution P (the same for all and connect u to the corresponding nodes as well as its ring successor. We prove that, for any distribution P, in a graph with n nodes and an expected number of long-range contacts per node constructed in this fashion, the expected number of steps for greedy routing is Ω((log2n)/lalog*n), for some constant a > 1. This improves an earlier lower bound of Ω((log2n)/llog log n) by Aspnes et al. and is very close to the upper bound of O((log2n)/l) achieved by greedy routing in Kleinberg's (one-dimensional) "small-world" networks, a particular instance of uniform ring-based random graphs.

References

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cover image ACM Conferences
PODC '07: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
August 2007
424 pages
ISBN:9781595936165
DOI:10.1145/1281100
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 12 August 2007

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Author Tags

  1. coupling
  2. greedy routing
  3. lower bound
  4. peer-to-peer
  5. random graphs
  6. small-worlds

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

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  • (2022)Greedy Routing in Circulant NetworksGraphs and Combinatorics10.1007/s00373-022-02489-938:3Online publication date: 16-Apr-2022
  • (2014)Tight lower bounds for greedy routing in higher-dimensional small-world gridsProceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/2634074.2634134(816-829)Online publication date: 5-Jan-2014
  • (2014)Greedy routing in small-world networks with power-law degreesDistributed Computing10.1007/s00446-014-0210-y27:4(231-253)Online publication date: 1-Aug-2014
  • (2010)Structured overlay for heterogeneous environmentsACM Transactions on Autonomous and Adaptive Systems10.1145/1671948.16719505:1(1-25)Online publication date: 25-Feb-2010
  • (2009)Brief announcementProceedings of the 28th ACM symposium on Principles of distributed computing10.1145/1582716.1582776(300-301)Online publication date: 10-Aug-2009
  • (2009)Tight lower bounds for greedy routing in uniform small world ringsProceedings of the forty-first annual ACM symposium on Theory of computing10.1145/1536414.1536494(591-600)Online publication date: 31-May-2009
  • (2008)Polylogarithmic network navigability using compact metrics with small stretchProceedings of the twentieth annual symposium on Parallelism in algorithms and architectures10.1145/1378533.1378542(62-69)Online publication date: 1-Jun-2008
  • (2008)Networks Become Navigable as Nodes Move and ForgetProceedings of the 35th international colloquium on Automata, Languages and Programming - Volume Part I10.1007/978-3-540-70575-8_12(133-144)Online publication date: 7-Jul-2008
  • (2007)Small worlds as navigable augmented networksProceedings of the 15th annual European conference on Algorithms10.5555/1778580.1778583(2-11)Online publication date: 8-Oct-2007

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