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Analyzing Network Coding (Gossip) Made Easy

Author:

Bernhard HaeuplerAuthors Info & Claims

Journal of the ACM (JACM), Volume 63, Issue 3

Article No.: 26, Pages 1 - 22

https://doi.org/10.1145/2629696

Published: 22 August 2016 Publication History

Abstract

We introduce projection analysis—a new technique to analyze the stopping time of protocols that are based on random linear network coding (RLNC). Projection analysis drastically simplifies, extends, and strengthens previous results on RLNC gossip protocols. We analyze RLNC gossip in a general framework for network and communication models that encompasses and unifies the models used previously in this context. We show, in most settings for the first time, that the RLNC gossip converges with high probability in optimal time. Most stopping times are of the form O(k + T), where k is the number of messages to be distributed and T is the time it takes to disseminate one message. This means RLNC gossip achieves “perfect pipelining.”

Our analysis directly extends to highly dynamic networks in which the topology can change completely at any time. This remains true, even if the network dynamics are controlled by a fully adaptive adversary that knows the complete network state. Virtually nothing besides simple O(kT) sequential flooding protocols was previously known for such a setting.

While RLNC gossip works in this wide variety of networks our analysis remains the same and extremely simple. This contrasts with more complex proofs that were put forward to give less strong results for various special cases.

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Index Terms

Analyzing Network Coding (Gossip) Made Easy
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows
  2. Randomness, geometry and discrete structures

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cover image Journal of the ACM

Journal of the ACM Volume 63, Issue 3

September 2016

303 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2957788

Editor:
Éva Tardos
Cornell University

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Copyright © 2016 ACM.

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 the author(s) 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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Publication History

Published: 22 August 2016

Accepted: 01 January 2016

Revised: 01 August 2015

Received: 01 September 2011

Published in JACM Volume 63, Issue 3

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Cited By

Gonen MLangberg MSprintson A(2022)Latency and Alphabet Size in the Context of Multicast Network CodingIEEE Transactions on Information Theory10.1109/TIT.2022.316039868:7(4289-4300)Online publication date: Jul-2022
https://doi.org/10.1109/TIT.2022.3160398
Dotan MPignolet YSchmid STochner SZohar A(2021)Survey on Blockchain NetworkingACM Computing Surveys10.1145/345316154:5(1-34)Online publication date: 25-May-2021
https://dl.acm.org/doi/10.1145/3453161
Zimmerling MMottola LSantini S(2020)Synchronous Transmissions in Low-Power WirelessACM Computing Surveys10.1145/341015953:6(1-39)Online publication date: 6-Dec-2020
https://dl.acm.org/doi/10.1145/3410159
Dotan MPignolet YSchmid STochner SZohar AVolkamer MWressnegger C(2020)SOKProceedings of the 15th International Conference on Availability, Reliability and Security10.1145/3407023.3407043(1-13)Online publication date: 25-Aug-2020
https://dl.acm.org/doi/10.1145/3407023.3407043
Haeupler BWajc DZuzic G(2020)Network Coding Gaps for Completion Times of Multiple Unicasts2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS46700.2020.00053(494-505)Online publication date: Nov-2020
https://doi.org/10.1109/FOCS46700.2020.00053
Herrmann CMager FZimmerling M(2018)MixerProceedings of the 16th ACM Conference on Embedded Networked Sensor Systems10.1145/3274783.3274849(145-158)Online publication date: 4-Nov-2018
https://dl.acm.org/doi/10.1145/3274783.3274849
Haeupler BMohapatra JSu HNewport CKeidar I(2018)Optimal Gossip Algorithms for Exact and Approximate Quantile ComputationsProceedings of the 2018 ACM Symposium on Principles of Distributed Computing10.1145/3212734.3212770(179-188)Online publication date: 23-Jul-2018
https://dl.acm.org/doi/10.1145/3212734.3212770
Gonen MLangberg MSprintson A(2018)Latency and Alphabet Size in the Context of Multicast Network Coding2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)10.1109/ALLERTON.2018.8636026(212-218)Online publication date: Oct-2018
https://doi.org/10.1109/ALLERTON.2018.8636026

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