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On the Impact of Identifiers on Local Decision

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Principles of Distributed Systems (OPODIS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7702))

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Abstract

The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that are inherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2) topological information gathering. In the context of local computation, i.e., when nodes can gather information only from nodes at bounded distances, some insight regarding the role of identities has been established. For instance, it was shown that, for large classes of construction problems, the role of the identities can be rather small. However, for the identities to play no role, some other kinds of mechanisms for breaking symmetry must be employed, such as edge-labeling or sense of direction. When it comes to local distributed decision problems, the specification of the decision task does not seem to involve symmetry breaking. Therefore, it is expected that, assuming nodes can gather sufficient information about their neighborhood, one could get rid of the identities, without employing extra mechanisms for breaking symmetry. We tackle this question in the framework of the \(\mathcal{LOCAL}\) model.

Let LD be the class of all problems that can be decided in a constant number of rounds in the \(\mathcal{LOCAL}\) model. Similarly, let LD* be the class of all problems that can be decided at constant cost in the anonymous variant of the \(\mathcal{LOCAL}\) model, in which nodes have no identities, but each node can get access to the (anonymous) ball of radius t around it, for any t, at a cost of t. It is clear that LD* ⊆ LD. We conjecture that LD*=LD. In this paper, we give several evidences supporting this conjecture. In particular, we show that it holds for hereditary problems, as well as when the nodes know an arbitrary upper bound on the total number of nodes. Moreover, we prove that the conjecture holds in the context of non-deterministic local decision, where nodes are given certificates (independent of the identities, if they exist), and the decision consists in verifying these certificates. In short, we prove that NLD*=NLD.

This work is supported by the Jules Verne Franco-Icelandic bilateral scientific framework.

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Authors and Affiliations

  1. CNRS and University Paris Diderot, France

    Pierre Fraigniaud & Amos Korman

  2. ICE-TCS, School of Computer Science, Reykjavik University, Iceland

    Magnús M. Halldórsson

Authors
  1. Pierre Fraigniaud
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  2. Magnús M. Halldórsson
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  3. Amos Korman
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Automatica e Gestionale, Università degli Studi di Roma “La Sapienza”, Via Ariosto 25, 00168, Rome, Italy

    Roberto Baldoni

  2. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Street, K1N 6N5, Ottawa, ON, Canada

    Paola Flocchini

  3. Electrical and Computing Engineering Dept., Virginia Technical University, 302 Whittemore Street, 24061, Blacksburg, VA, USA

    Ravindran Binoy

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Fraigniaud, P., Halldórsson, M.M., Korman, A. (2012). On the Impact of Identifiers on Local Decision. In: Baldoni, R., Flocchini, P., Binoy, R. (eds) Principles of Distributed Systems. OPODIS 2012. Lecture Notes in Computer Science, vol 7702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35476-2_16

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  • DOI: https://doi.org/10.1007/978-3-642-35476-2_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35475-5

  • Online ISBN: 978-3-642-35476-2

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