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International Colloquium on Structural Information and Communication Complexity

SIROCCO 2019: Structural Information and Communication Complexity pp 262–276Cite as

Faster Construction of Overlay Networks

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11639))

Abstract

We consider the problem of transforming any weakly connected overlay network of polylogarithmic degree into a topology of logarithmic diameter. The overlay network is modeled as a directed graph, in which messages are sent in synchronous rounds, and new edges can be established by sending node identifiers. However, every node can only send and receive a polylogarithmic number of bits in each round, which makes the naive approach of introducing all neighbors to each other until the network forms a clique infeasible. We present an algorithm that takes time \(O(\log ^{3/2} n)\), w.h.p. At the heart of our algorithm lies a deterministic strategy to group and merge large components of nodes, but we make use of randomized load-balancing techniques to keep the communication load of each node low. To the best of our knowledge, this is the first algorithm to improve upon the algorithm by Angluin et al. [SPAA 2005], which solves the problem in time \(O(\log ^2 n)\), and comes closer to the \(\varOmega (\log n)\) lower bound.

This work is partially supported by the German Research Foundation (DFG) within the CRC 901 “On-The-Fly Computing” (project number 160364472-SFB901).

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Notes

  1. 1.

    Note that for our algorithm polylogarithmic memory and a small number of local computations is sufficient.

  2. 2.

    We say an event holds with high probability (w.h.p.), if it holds with probability at least \(1- 1/n^c\) for any fixed constant \(c > 0\).

  3. 3.

    An aggregate function f is called distributive if there is an aggregate function g such that for any partition \(A_1,...,A_k \subset A\), it holds \(f(A) = g(f(A_1),...,f(A_k))\) (e.g., Max, Min, and Sum are distributive).

  4. 4.

    For the first subphase, we have to assume that every supernode is of size at least 2 already, which can, e.g., be ensured by letting each node simulate two virtual nodes.

  5. 5.

    To agree on a suitable random hash function h, \(\ell _v\) needs to broadcast \(O(\log ^2 n)\) random bits to all nodes in \(B_v\) (see [4, 7] for details).

References

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Authors and Affiliations

  1. Paderborn University, Paderborn, Germany

    Thorsten Götte, Kristian Hinnenthal & Christian Scheideler

Authors
  1. Thorsten Götte
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  2. Kristian Hinnenthal
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  3. Christian Scheideler
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Corresponding author

Correspondence to Kristian Hinnenthal .

Editor information

Editors and Affiliations

  1. Technion, Haifa, Israel

    Keren Censor-Hillel

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

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Götte, T., Hinnenthal, K., Scheideler, C. (2019). Faster Construction of Overlay Networks. In: Censor-Hillel, K., Flammini, M. (eds) Structural Information and Communication Complexity. SIROCCO 2019. Lecture Notes in Computer Science(), vol 11639. Springer, Cham. https://doi.org/10.1007/978-3-030-24922-9_18

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  • DOI: https://doi.org/10.1007/978-3-030-24922-9_18

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  • Print ISBN: 978-3-030-24921-2

  • Online ISBN: 978-3-030-24922-9

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