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Information Spreading in Dynamic Networks Under Oblivious Adversaries

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Distributed Computing (DISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9888))

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Abstract

We study the problem of gossip in dynamic networks controlled by an adversary that can modify the network arbitrarily from one round to another, provided that the network is always connected. In the gossip problem, there are n tokens arbitrarily distributed among the n network nodes, and the goal is to disseminate all the n tokens to every node. Our focus is on token-forwarding algorithms, which do not manipulate tokens in any way other than storing, copying, and forwarding them. An important open question is whether gossip can be realized by a distributed protocol that can do significantly better than an easily achievable bound of \(O(n^2)\) rounds.

In this paper, we study oblivious adversaries, i.e., those that are oblivious to the random choices made by the protocol. We consider Rand-Diff, a natural distributed algorithm in which neighbors exchange a token chosen uniformly at random from the difference of their token sets. We present an \(\tilde{\varOmega }(n^{3/2})\) lower bound for Rand-Diff under an oblivious adversary. We also present an \(\tilde{\varOmega }(n^{4/3})\) lower bound under a stronger notion of oblivious adversary for a class of randomized distributed algorithms—symmetric knowledge-based algorithms— in which nodes make token transmission decisions based entirely on the sets of tokens they possess over time. On the positive side, we present a centralized algorithm that completes gossip in \(\tilde{O}(n^{3/2})\) rounds with high probability, under any oblivious adversary. We also show an \(\tilde{O}(n^{5/3})\) upper bound for Rand-Diff in a restricted class of oblivious adversaries, which we call paths-respecting, that may be of independent interest.

J.A. was supported by IIT Madras New Faculty Seed Grant, IIT Madras Exploratory Research Project, and Indo-German Max Planck Center for Computer Science (IMPECS). G.P. was partially supported by NSF grants CCF-1527867 and CCF-1540512. M.L. and R.R were partially supported by grants NSF CCF-1422715, NSF CCF-1535929, and ONR N00014-12-1-1001.

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Notes

  1. 1.

    In each round of the strongly adaptive adversary model, each node first chooses a token to broadcast to all its neighbors, and then the adversary chooses a connected network for that round with the knowledge of the tokens chosen by each node.

  2. 2.

    The notation \(\tilde{\varOmega }\) hides polylogarithmic factors in the denominator and \(\tilde{O}\) hides polylogarithmic factors in the numerator.

  3. 3.

    Actually, [15] shows the \(O(n \mathrm {polylog}(n))\) bound applies even for a weaker protocol called Sym-Diff, where the token exchanged between two neighbouring nodes is a random token from the symmetric difference of the token sets of the two nodes.

  4. 4.

    Throughout, by “with high probability” or whp, we mean with probability at least \(1 - 1/n^c\), where the constant c can be made sufficiently large by adjusting other parameters in the analysis.

  5. 5.

    Indeed, an infrastructure-based model captures many real-world scenarios involving an underlying communication network with dynamics restricted to the network edges. This is unlike the case of a general oblivious adversary where the graph can change arbitrarily from round to round.

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Authors and Affiliations

  1. IIT Madras, Chennai, 600036, India

    John Augustine

  2. Ben-Gurion University of the Negev, 84105, Beersheba, Israel

    Chen Avin

  3. Northeastern University, Boston, 02115, USA

    Mehraneh Liaee & Rajmohan Rajaraman

  4. University of Houston, Houston, TX, 77204, USA

    Gopal Pandurangan

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  1. John Augustine
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  2. Chen Avin
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  3. Mehraneh Liaee
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  4. Gopal Pandurangan
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  5. Rajmohan Rajaraman
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Correspondence to Rajmohan Rajaraman .

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Editors and Affiliations

  1. LABRI, Univ of Bordeaux LABRI, Talence Cedex, France

    Cyril Gavoille

  2. CNRS, Universite Bordeaux 1 CNRS, Talence Cedex, France

    David Ilcinkas

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Augustine, J., Avin, C., Liaee, M., Pandurangan, G., Rajaraman, R. (2016). Information Spreading in Dynamic Networks Under Oblivious Adversaries. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_29

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  • DOI: https://doi.org/10.1007/978-3-662-53426-7_29

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