Randomized gossip algorithms for solving Laplacian systems

Anastasios Zouzias, Nikolaos Freris

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We consider the problem of solving a Laplacian system of equations Lx = b in a distributed fashion, where L is the Laplacian of the communication graph. Solving Laplacian systems arises in a number of applications including consensus, distributed control, clock synchronization, localization and calculating effective resistances, to name a few. We leverage our analysis on a randomized variant of Kaczmarz's algorithm to propose a distributed asynchronous gossip algorithm with expected exponential convergence. We quantify the convergence rate depending solely on properties of the network topology, and further propose an accelerated version that scales favorably for larger networks. Our approach naturally extends to least-squares estimation of general linear systems where each row/column is assigned to nodes of a given network. Last but not least, we show that average consensus is a special case in our framework.

    Original languageEnglish (US)
    Title of host publication2015 European Control Conference, ECC 2015
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages1920-1925
    Number of pages6
    ISBN (Electronic)9783952426937
    DOIs
    StatePublished - Nov 16 2015
    EventEuropean Control Conference, ECC 2015 - Linz, Austria
    Duration: Jul 15 2015Jul 17 2015

    Other

    OtherEuropean Control Conference, ECC 2015
    CountryAustria
    CityLinz
    Period7/15/157/17/15

    Fingerprint

    Linear systems
    Clocks
    Synchronization
    Topology
    Communication

    Keywords

    • Clock synchronization
    • Consensus
    • Cyberphysical systems
    • Distributed algorithms
    • Gossip algorithms
    • Laplacian systems
    • Randomized algorithms

    ASJC Scopus subject areas

    • Control and Systems Engineering

    Cite this

    Zouzias, A., & Freris, N. (2015). Randomized gossip algorithms for solving Laplacian systems. In 2015 European Control Conference, ECC 2015 (pp. 1920-1925). [7330819] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ECC.2015.7330819

    Randomized gossip algorithms for solving Laplacian systems. / Zouzias, Anastasios; Freris, Nikolaos.

    2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1920-1925 7330819.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Zouzias, A & Freris, N 2015, Randomized gossip algorithms for solving Laplacian systems. in 2015 European Control Conference, ECC 2015., 7330819, Institute of Electrical and Electronics Engineers Inc., pp. 1920-1925, European Control Conference, ECC 2015, Linz, Austria, 7/15/15. https://doi.org/10.1109/ECC.2015.7330819
    Zouzias A, Freris N. Randomized gossip algorithms for solving Laplacian systems. In 2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 1920-1925. 7330819 https://doi.org/10.1109/ECC.2015.7330819
    Zouzias, Anastasios ; Freris, Nikolaos. / Randomized gossip algorithms for solving Laplacian systems. 2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 1920-1925
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