Time Complexity of Distributed Topological Self-stabilization: The Case of Graph Linearization

  • Dominik Gall
  • Riko Jacob
  • Andrea Richa
  • Christian Scheideler
  • Stefan Schmid
  • Hanjo Täubig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)


Topological self-stabilization is an important concept to build robust open distributed systems (such as peer-to-peer systems) where nodes can organize themselves into meaningful network topologies. The goal is to devise distributed algorithms that converge quickly to such a desirable topology, independently of the initial network state. This paper proposes a new model to study the parallel convergence time. Our model sheds light on the achievable parallelism by avoiding bottlenecks of existing models that can yield a distorted picture. As a case study, we consider local graph linearization—i.e., how to build a sorted list of the nodes of a connected graph in a distributed and self-stabilizing manner. We propose two variants of a simple algorithm, and provide an extensive formal analysis of their worst-case and best-case parallel time complexities, as well as their performance under a greedy selection of the actions to be executed.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dominik Gall
    • 1
  • Riko Jacob
    • 1
  • Andrea Richa
    • 2
  • Christian Scheideler
    • 3
  • Stefan Schmid
    • 4
  • Hanjo Täubig
    • 1
  1. 1.Institut für InformatikTU MünchenGarchingGermany
  2. 2.Dept. Computer Science and EngineeringArizona State UniversityTempeUSA
  3. 3.Dept. Computer ScienceUniversity of PaderbornPaderbornGermany
  4. 4.Deutsche Telekom LaboratoriesTU BerlinBerlinGermany

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