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https://doi.org/10.1007/978-3-...
Part of book or chapter of book . 2016 . Peer-reviewed
License: Springer TDM
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gradual stabilization under tau dynamics

Authors: Altisen, Karine; Devismes, Stéphane; Durand, Anaïs; Petit, Franck;

gradual stabilization under tau dynamics

Abstract

International audience; We introduce the notion of gradually stabilizing algorithm as any self-stabilizing algorithm achieving the following additional feature. If at most τ dynamic steps occur starting from a legitimate configuration, a gradually stabilizing algorithm first quickly recover to a configuration from which a specification offering a minimum quality of service is satisfied. It then gradually converges to specifications offering stronger and stronger safety guarantees until reaching a configuration (1) from which its initial (strong) specification is satisfied again, and (2) where it is ready to achieve gradual convergence again in case of up to $\tau$ new dynamic steps. By definition, a gradually stabilizing algorithm is also self-stabilizing. So, it still recovers within finite time (yet more slowly) after any other finite number of transient faults, including for example more than $\tau$ dynamic steps or other failure patterns such as memory corruptions, for example.We illustrate this new property by considering three variants of a synchronization problem respectively called strong, weak, and partial weak unison. We propose a self-stabilizing algorithm which achieves gradual stabilization in the sense that after one dynamic step from a configuration which is legitimate for the strong unison, it immediately satisfies the specification of partial weak unison, then converges to the specification of weak unison in at most one round, and finally retrieves, after at most (mu+1) D1 + 1 additional rounds, a configuration (1) from which the specification of strong unison is satisfied, and (2) where it is ready to achieve gradual convergence again in case of another dynamic step. D1 is the diameter of the network after the dynamic step, and mu is a parameter satisfying mu >= n + #J, where n is the initial number of processes and #J is an upper bound on the number of processes that join the system during a dynamic step.

Country
France
Keywords

synchronization problems, safe-convergence, superstabilization, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], gradual stabilization, unison, Self-stabilization

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average