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Fault-Tolerant Rendezvous in Networks

  • Conference paper
Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8573))

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Abstract

Two mobile agents, starting from different nodes of an unknown network, have to meet at the same node. Agents move in synchronous rounds using a deterministic algorithm. Each agent has a different label, which it can use in the execution of the algorithm, but it does not know the label of the other agent. Agents do not know any bound on the size of the network. In each round an agent decides if it remains idle or if it wants to move to one of the adjacent nodes. Agents are subject to delay faults: if an agent incurs a fault in a given round, it remains in the current node, regardless of its decision. If it planned to move and the fault happened, the agent is aware of it. We consider three scenarios of fault distribution: random (independently in each round and for each agent with constant probability 0 < p < 1), unbounded adversarial (the adversary can delay an agent for an arbitrary finite number of consecutive rounds) and bounded adversarial (the adversary can delay an agent for at most c consecutive rounds, where c is unknown to the agents). The quality measure of a rendezvous algorithm is its cost, which is the total number of edge traversals.

For random faults, we show an algorithm with cost polynomial in the size n of the network and polylogarithmic in the larger label L, which achieves rendezvous with very high probability in arbitrary networks. By contrast, for unbounded adversarial faults we show that rendezvous is not feasible, even in the class of rings. Under this scenario we give a rendezvous algorithm with cost O(nℓ), where ℓ is the smaller label, working in arbitrary trees, and we show that Ω(ℓ) is the lower bound on rendezvous cost, even for the two-node tree. For bounded adversarial faults, we give a rendezvous algorithm working for arbitrary networks, with cost polynomial in n, and logarithmic in the bound c and in the larger label L.

Keywords: rendezvous, deterministic algorithm, mobile agent, delay fault.

The full version of the paper is available at http://arxiv.org/abs/1402.2760

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Author information

Authors and Affiliations

  1. LIF, CNRS & Aix-Marseille University, Marseille, France

    Jérémie Chalopin & Arnaud Labourel

  2. MIS, Université de Picardie Jules Verne, France

    Yoann Dieudonné

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

    Andrzej Pelc

Authors
  1. Jérémie Chalopin
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  2. Yoann Dieudonné
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  3. Arnaud Labourel
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  4. Andrzej Pelc
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK,

    Elias Koutsoupias

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Chalopin, J., Dieudonné, Y., Labourel, A., Pelc, A. (2014). Fault-Tolerant Rendezvous in Networks. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_35

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  • DOI: https://doi.org/10.1007/978-3-662-43951-7_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43950-0

  • Online ISBN: 978-3-662-43951-7

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