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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)

Abstract

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.

Keywords

Random Graph Shared Variable Distribute Hash Table Longe Edge Linearization Step 
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-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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