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Transience Bounds for Distributed Algorithms

  • Conference paper
Book cover Formal Modeling and Analysis of Timed Systems (FORMATS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8053))

Abstract

A large variety of distributed systems, like some classical synchronizers, routers, or schedulers, have been shown to have a periodic behavior after an initial transient phase (Malka and Rajsbaum, WDAG 1991). In fact, each of these systems satisfies recurrence relations that turn out to be linear as soon as we consider max-plus or min-plus algebra. In this paper, we give a new proof that such systems are eventually periodic and a new upper bound on the length of the initial transient phase. Interestingly, this is the first asymptotically tight bound that is linear in the system size for various classes of systems. Another significant benefit of our approach lies in the straightforwardness of arguments: The proof is based on an easy convolution lemma borrowed from Nachtigall (Math. Method. Oper. Res. 46) instead of purely graph-theoretic arguments and involved path reductions found in all previous proofs.

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Author information

Authors and Affiliations

  1. CNRS, LIX, École polytechnique, France

    Bernadette Charron-Bost & Thomas Nowak

  2. ECS Group, TU Wien, Austria

    Matthias Függer

Authors
  1. Bernadette Charron-Bost
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  2. Matthias Függer
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  3. Thomas Nowak
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Editor information

Editors and Affiliations

  1. Facultad de Ciencias Exactas y Naturales, Departamento de Computación, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Intendente Güiraldes 2160, C1428EGA, Buenos Aires, Argentina

    Víctor Braberman

  2. LSV, CNRS & ENS de Cachan, 61, avenue du Président Wilson, 94235, Cachan Cedex, France

    Laurent Fribourg

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Charron-Bost, B., Függer, M., Nowak, T. (2013). Transience Bounds for Distributed Algorithms. In: Braberman, V., Fribourg, L. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2013. Lecture Notes in Computer Science, vol 8053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40229-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-40229-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40228-9

  • Online ISBN: 978-3-642-40229-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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