Maintaining a Spanning Forest in Highly Dynamic Networks: The Synchronous Case

  • Matthieu Barjon
  • Arnaud Casteigts
  • Serge Chaumette
  • Colette Johnen
  • Yessin M. Neggaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8878)


Highly dynamic networks are characterized by frequent changes in the availability of communication links. Many of these networks are in general partitioned into several components that keep splitting and merging continuously and unpredictably. We present an algorithm that strives to maintain a forest of spanning trees in such networks, without any kind of assumption on the rate of changes. Our algorithm is the adaptation of a coarse-grain interaction algorithm (Casteigts et al., 2013) to the synchronous message passing model (for dynamic networks). While the high-level principles of the coarse-grain variant are preserved, the new algorithm turns out to be significantly more complex. In particular, it involves a new technique that consists of maintaining a distributed permutation of the set of all nodes IDs throughout the execution. The algorithm also inherits the properties of its original variant: It relies on purely localized decisions, for which no global information is ever collected at the nodes, and yet it maintains a number of critical properties whatever the frequency and scale of the changes. In particular, the network remains always covered by a spanning forest in which 1) no cycle can ever appear, 2) every node belongs to a tree, and 3) after an arbitrary number of edge disappearance, all maximal subtrees immediately restore exactly one token (at their root). These properties are ensured whatever the dynamics, even if it keeps going for an arbitrary long period of time. Optimality is not the focus here, however the number of tree per components – the metric of interest here – eventually converges to one if the network stops changing (which is never expected to happen, though). The algorithm correctness is proven and its behavior is tested through experimentation.


Span Tree Dynamic Network Minimum Span Tree Span Forest Merging Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Matthieu Barjon
    • 1
  • Arnaud Casteigts
    • 1
  • Serge Chaumette
    • 1
  • Colette Johnen
    • 1
  • Yessin M. Neggaz
    • 1
  1. 1.LaBRIUniversity of BordeauxFrance

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