Time complexity of distributed topological self-stabilization: the case of graph linearization

  • Authors:

  • Dominik Gall;Riko Jacob;Andrea Richa;Christian Scheideler;Stefan Schmid;Hanjo Täubig

  • Affiliations:

  • Institut für Informatik, TU München, Garching, Germany;Institut für Informatik, TU München, Garching, Germany;Dept. Computer Science and Engineering, Arizona State University, Tempe;Dept. Computer Science, University of Paderborn, Paderborn, Germany;Deutsche Telekom Laboratories, TU Berlin, Berlin, Germany;Institut für Informatik, TU München, Garching, Germany

  • Venue:
  • LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
  • Year:
  • 2010

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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.