A Note on the Parallel Runtime of Self-Stabilizing Graph Linearization

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 where nodes forward, insert, and delete links to neighboring nodes, and that converge quickly to such a desirable topology, independently of the initial network configuration. This article 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. In order to study the main structure and properties of our model, we propose two variants of a most simple local linearization algorithm. For each of these variants, we present analyses of the worst-case and best-case parallel time complexities, as well as the performance under a greedy selection of the actions to be executed. It turns out that the analysis is non-trivial despite the simple setting, and to complement our formal insights we report on our experiments which indicate that the runtimes may be better in the average case.

Original languageEnglish (US)
Pages (from-to)110-135
Number of pages26
JournalTheory of Computing Systems
Volume55
Issue number1
DOIs
StatePublished - 2014

Fingerprint

Linearization
Graph in graph theory
Vertex of a graph
Topology
Self-stabilization
Peer-to-peer Systems
Convergence Time
Open Systems
Distributed Algorithms
Parallel algorithms
Network Topology
Model
Time Complexity
Parallelism
Connected graph
Distributed Systems
Complement
Stabilization
Converge
Configuration

Keywords

  • Distributed algorithms
  • Distributed systems
  • Overlay networks
  • Peer-to-peer systems
  • Performance
  • Self-stabilization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

A Note on the Parallel Runtime of Self-Stabilizing Graph Linearization. / Gall, Dominik; Jacob, Riko; Richa, Andrea; Scheideler, Christian; Schmid, Stefan; Täubig, Hanjo.

In: Theory of Computing Systems, Vol. 55, No. 1, 2014, p. 110-135.

Research output: Contribution to journalArticle

Gall, Dominik ; Jacob, Riko ; Richa, Andrea ; Scheideler, Christian ; Schmid, Stefan ; Täubig, Hanjo. / A Note on the Parallel Runtime of Self-Stabilizing Graph Linearization. In: Theory of Computing Systems. 2014 ; Vol. 55, No. 1. pp. 110-135.
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