*Time- and Space-Efficient Self-Stabilizing Algorithms*. PhD Thesis, Hamburg University of Technology, Hamburg, Germany, 2012.

# Bernd Hauck

Dr. rer. nat. Bernd Hauck

I work as a research assistant at the Institute of Telematics since June 2007.

## Projects

- TSSSA - Time- and Space-efficient Self-Stabilizing Algorithms

## Publications

Bernd Hauck.

@PhdThesis{Telematik_Hauck_2012_Diss,
author = {Bernd Hauck},
title = {Time- and Space-Efficient Self-Stabilizing Algorithms},
publisher = {Cuvillier Verlag, G{\"o}ttingen, Germany},
school = {Hamburg University of Technology},
address = {Hamburg, Germany},
edition = {1st},
year = 2012,
isbn = {978-3-95404-324-8},
}

**Abstract**: Self-stabilization is a general approach to design a system to tolerate arbitrary transient faults. This thesis presents new time- and space-efficient self-stabilizing algorithms for well-known problems in graph theory and provides new complexity analyzes for existing algorithms. The main focus of this thesis is on the proof techniques used in the complexity analyzes and the design of the algorithms.

Volker Turau and Bernd Hauck. A new Analysis of a Self-Stabilizing Maximum Weight Matching Algorithm with Approximation Ratio 2.

*Theoretical Computer Science*, 412(40):5527–5540, September 2011. Stabilization, Safety and Security.@Article{Telematik_HT_2010_TCS_Matching,
author = {Volker Turau and Bernd Hauck},
title = {A new Analysis of a Self-Stabilizing Maximum Weight Matching Algorithm with Approximation Ratio 2},
pages = {5527-5540},
journal = {Theoretical Computer Science},
volume = {412},
number = {40},
month = sep,
year = 2011,
keywords = {Self-stabilizing algorithms, approximation algorithm, weighted matching, distributed algorithms},
issn = {0304-3975},
note = {Stabilization, Safety and Security},
}

**Abstract**: The maximum weight matching problem is a fundamental problem in graph theory with a variety of important applications. Recently Manne and Mjelde presented the first self-stabilizing algorithm computing a 2-approximation of the optimal solution. They established that their algorithm stabilizes after O(2^n) (resp. O(3^n)) moves under a central (resp. distributed) scheduler. This paper contributes a new analysis improving these bounds considerably. In particular it is shown that the algorithm stabilizes after O(nm) moves under the central scheduler and that a modified version of the algorithm also stabilizes after O(nm) moves under the distributed scheduler. The paper presents a new proof technique based on graph reduction to analyze the complexity of self-stabilizing algorithms.

Volker Turau and Bernd Hauck. A fault-containing self-stabilizing (3 - 2/(Delta+1))-approximation algorithm for vertex cover in anonymous networks.

*Theoretical Computer Science*, 412(33):4361–4371, 2011.@Article{Telematik_HT_2011_TCSVC,
author = {Volker Turau and Bernd Hauck},
title = {A fault-containing self-stabilizing (3 - 2/(Delta+1))-approximation algorithm for vertex cover in anonymous networks},
pages = {4361-4371},
journal = {Theoretical Computer Science},
volume = {412},
number = {33},
year = 2011,
keywords = {Self-stabilizing algorithms, Fault tolerance, Distributed algorithms, Graph algorithms},
}

**Abstract**: The non-computability of many distributed tasks in anonymous networks is well known. This paper presents a deterministic self-stabilizing algorithm to compute a 3 - (2 / (Delta+1))-approximation of a minimum vertex cover in anonymous networks. The algorithm operates under the distributed unfair scheduler, stabilizes after O(n+m) moves respectively O(Delta) rounds, and requires O(log n) storage per node. Recovery from a single fault is reached within a constant time and the contamination number is O(Delta). For trees the algorithm computes a 2-approximation of a minimum vertex cover.

The complete list of publications is available separately.