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Computing the Dynamic Diameter of Non-Deterministic Dynamic Networks is Hard

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Algorithms for Sensor Systems (ALGOSENSORS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 8847))

Abstract

A dynamic network is a communication network whose communication structure can evolve over time. The dynamic diameter is the counterpart of the classical static diameter, it is the maximum time needed for a node to causally influence any other node in the network. We consider the problem of computing the dynamic diameter of a given dynamic network. If the evolution is known a priori, that is if the network is deterministic, it is known it is quite easy to compute this dynamic diameter. If the evolution is not known a priori, that is if the network is non-deterministic, we show that the problem is hard to solve or approximate. In some cases, this hardness holds also when there is a static connected subgraph for the dynamic network.

In this note, we consider an important subfamily of non-deterministic dynamic networks: the time-homogeneous dynamic networks. We prove that it is hard to compute and approximate the value of the dynamic diameter for time-homogeneous dynamic networks.

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Authors and Affiliations

  1. Aix-Marseille Université, CNRS, LIF UMR 7279, 13000, Marseille, France

    Emmanuel Godard & Dorian Mazauric

Authors
  1. Emmanuel Godard
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  2. Dorian Mazauric
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Corresponding author

Correspondence to Emmanuel Godard .

Editor information

Editors and Affiliations

  1. Stony Brook University, Stonybrook, New York, USA

    Jie Gao

  2. University of Arizona, Tucson, Arizona, USA

    Alon Efrat

  3. TU Braunschweig, Braunschweig, Niedersachsen, Germany

    Sándor P. Fekete

  4. Rutgers University, New Brunswick, New Jersey, USA

    Yanyong Zhang

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Godard, E., Mazauric, D. (2015). Computing the Dynamic Diameter of Non-Deterministic Dynamic Networks is Hard. In: Gao, J., Efrat, A., Fekete, S., Zhang, Y. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2014. Lecture Notes in Computer Science(), vol 8847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46018-4_6

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  • DOI: https://doi.org/10.1007/978-3-662-46018-4_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46017-7

  • Online ISBN: 978-3-662-46018-4

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