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Communication Complexity of Consensus in Anonymous Message Passing Systems

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Principles of Distributed Systems (OPODIS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7109))

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Abstract

We consider the message complexity of achieving consensus in synchronous anonymous message passing systems. Unlabeled processors (nodes) communicate through links of a network. In each round every processor can exchange messages with all neighbors and the duration of each transmission is one round. An adversary wakes up some subset of processors at possibly different times and assigns them arbitrary numerical input values. All other processors are dormant and do not have input values. Any message wakes up a dormant processor. The goal of consensus is to wake up all processors and have them agree on one of the input values. We seek deterministic consensus algorithms using as few messages as possible. As opposed to most of the literature on consensus, the difficulty of our scenario are not faults (we assume that the network is fault-free) but the arbitrary network topology combined with the anonymity of nodes.

For unknown n-node networks we show a consensus algorithm using O(n 2) messages; this complexity is optimal for this class. We show that if the network is known, then the complexity of consensus decreases significantly. Our main contribution is an algorithm that uses O(n 3/2log2 n) messages on any n-node network and we show that some networks require Ω(nlogn) messages to achieve consensus. We also observe that availability of distinct labels of nodes helps to improve complexity of consensus for known networks but has no effect for the class of unknown networks. Indeed, even with labeled nodes, Ω(n 2) messages are sometimes necessary if the network is unknown but for known labeled networks consensus can be always achieved with O(n) messages.

This work was done during the visit of Emanuele G. Fusco at the Research Chair in Distributed Computing of the Université du Québec en Outaouais.

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Author information

Authors and Affiliations

  1. Computer Science Department, Sapienza University of Rome, 00198, Rome, Italy

    Emanuele G. Fusco

  2. Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec, J8X 3X7, Canada

    Andrzej Pelc

Authors
  1. Emanuele G. Fusco
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  2. Andrzej Pelc
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Editor information

Editors and Affiliations

  1. Institute IMDEA Networks, Avenida del Mar Mediterraneo, 22, 28918, Leganes, Madrid, Spain

    Antonio Fernàndez Anta

  2. CEIICP, RETIS Lab, Scuola Superiore Sant’Anna, Via Moruzzi 1, 56127, Pisa, Italy

    Giuseppe Lipari

  3. Dependability Group (TSF), LAAS-CNRS, 7 av du colonel Roche, 31077, Toulouse, France

    Matthieu Roy

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© 2011 Springer-Verlag Berlin Heidelberg

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Fusco, E.G., Pelc, A. (2011). Communication Complexity of Consensus in Anonymous Message Passing Systems. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_14

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  • DOI: https://doi.org/10.1007/978-3-642-25873-2_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25872-5

  • Online ISBN: 978-3-642-25873-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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