### 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 language | English (US) |
---|---|

Pages (from-to) | 110-135 |

Number of pages | 26 |

Journal | Theory of Computing Systems |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### 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

*Theory of Computing Systems*,

*55*(1), 110-135. https://doi.org/10.1007/s00224-013-9504-x

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

Research output: Contribution to journal › Article

*Theory of Computing Systems*, vol. 55, no. 1, pp. 110-135. https://doi.org/10.1007/s00224-013-9504-x

}

TY - JOUR

T1 - A Note on the Parallel Runtime of Self-Stabilizing Graph Linearization

AU - Gall, Dominik

AU - Jacob, Riko

AU - Richa, Andrea

AU - Scheideler, Christian

AU - Schmid, Stefan

AU - Täubig, Hanjo

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Distributed algorithms

KW - Distributed systems

KW - Overlay networks

KW - Peer-to-peer systems

KW - Performance

KW - Self-stabilization

UR - http://www.scopus.com/inward/record.url?scp=84901826595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901826595&partnerID=8YFLogxK

U2 - 10.1007/s00224-013-9504-x

DO - 10.1007/s00224-013-9504-x

M3 - Article

AN - SCOPUS:84901826595

VL - 55

SP - 110

EP - 135

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 1

ER -