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Erschienen in:
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2014 | OriginalPaper | Buchkapitel

Iterative Approximate Consensus in the Presence of Byzantine Link Failures

verfasst von : Lewis Tseng, Nitin Vaidya

Erschienen in: Networked Systems

Verlag: Springer International Publishing

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Abstract

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free.
Recent work has addressed the problem of reaching approximate consensus in incomplete graphs with Byzantine nodes using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations [12, 21, 23, 24]. This paper addresses approximate consensus in the presence of Byzantine links. We extend our past work [21, 23] that provided exact characterization of graphs in which the iterative approximate consensus problem in the presence of Byzantine node failures is solvable. In particular, we prove a tight necessary and sufficient condition on the underlying communication graph for the existence of iterative approximate consensus algorithms under transient Byzantine link model [15, 16].

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Vorheriges Kapitel Fair Linking Mechanisms for Resource Allocation with Correlated Player Types
Nächstes Kapitel Practically Self-stabilizing Paxos Replicated State-Machine
Fußnoten
1
A graph \(G=(\mathcal {V}, \mathcal {E})\) is said to be \(k\)-edge connected, if \(G'=(\mathcal {V}, \mathcal {E}- X)\) is connected for all \(X \subseteq \mathcal {E}\) such that \(\left| X\right| < k\).
 
2
A graph \(G=(\mathcal {V}, \mathcal {E})\) is said to be \(k\)-node connected, if \(G'=(\mathcal {V}- X, \mathcal {E})\) is connected for all \(X \subseteq \mathcal {V}\) such that \(\left| X\right| < k\).
 
3
Unlike the “transient” failures in our model, the faulty links are assumed to be fixed throughout the execution of the algorithm in [19].
 
4
For example, the described case is possible in wireless network, if node \(i\)’s transmitter is broken while node \(i\)’s receiver and node \(j\)’s transmitter and receiver all function correctly.
 
5
\(N_i^F\) may be different for each iteration \(t\). For simplicity, the notation does not explicitly represent this dependence.
 
6
Intuitively, \(N_i^r\) corresponds to the links removed in some link-reduced graph. Thus, the superscript \(r\) in the notation stands for “removed.” Also, \(N_i^r\) may be different for each \(t\). For simplicity, the notation does not explicitly represent this dependence.
 
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Metadaten
Titel
Iterative Approximate Consensus in the Presence of Byzantine Link Failures
verfasst von
Lewis Tseng
Nitin Vaidya
Copyright-Jahr
2014
Buch
Networked Systems

Print ISBN: 978-3-319-09580-6

Electronic ISBN: 978-3-319-09581-3

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-319-09581-3_7