*Theoretical Computer Science*, 412(40):5527–5540, September 2011. Stabilization, Safety and Security.

# Publications

Journal Articles | Conference Contributions | PhD Theses | Technical Reports

## Journal Articles

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

@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.

Volker Turau and Bernd Hauck. A Self-Stabilizing Algorithm for Constructing Weakly Connected Minimal Dominating Sets.

*Information Processing Letters*, 109(14):763–767, 2009.@Article{Telematik_HT_2009_WCMDS,
author = {Volker Turau and Bernd Hauck},
title = {A Self-Stabilizing Algorithm for Constructing Weakly Connected Minimal Dominating Sets},
pages = {763-767},
journal = {Information Processing Letters},
volume = {109},
number = {14},
year = 2009,
keywords = {Self-stabilizing algorithms, Fault tolerance, Distributed algorithms, Graph algorithms},
issn = {0020-0190},
}

**Abstract**: This paper presents a new distributed self-stabilizing algorithm for the weakly connected minimal dominating set problem. It assumes a self-stabilizing algorithm to compute a breadth-first tree. Using an unfair distributed scheduler the algorithm stabilizes in at most O(nmA) moves, where A is the number of moves to construct a breadth-first tree. All previously known algorithms required an exponential number of moves.

## Conference Contributions

Volker Turau and Bernd Hauck. A Self-Stabilizing Approximation Algorithm for Vertex Cover in Anonymous Networks. In

*Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS'09)*, Springer, November 2009, pp. 341–353. Lyon, France.@InProceedings{Telematik_HT_2009_VC,
author = {Volker Turau and Bernd Hauck},
title = {A Self-Stabilizing Approximation Algorithm for Vertex Cover in Anonymous Networks},
booktitle = {Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS'09)},
pages = {341-353},
series = {Lecture Notes in Computer Science},
volume = {5873},
publisher = {Springer},
day = {3-6},
month = nov,
year = 2009,
location = {Lyon, France},
}

**Abstract**: This paper presents a deterministic self-stabilizing algorithm that computes a 3-approximation vertex cover in anonymous networks. It reaches a legal state after O(n+m) moves or 2n + 1 rounds respectively and recovers from a single fault within a constant containment time. The contamination number is 2 Delta + 1. An enhanced version of this algorithm achieves a 2-approximation on trees.

## PhD Theses

Bernd Hauck.

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

## Technical Reports

Bernd Hauck.

*Worst-Case Analysis of a Self-Stabilizing Algorithm Computing a Weakly Connected Minimal Dominating Set*. Technical Report urn:nbn:de:gbv:830-tubdok-5126, Hamburg University of Technology, Hamburg, Germany, October 2008.@TechReport{Telematik_Hauck_2008_WorstCaseSelfStabilizingWeaklyConnectedMDSet,
author = {Bernd Hauck},
title = {Worst-Case Analysis of a Self-Stabilizing Algorithm Computing a Weakly Connected Minimal Dominating Set},
number = {urn:nbn:de:gbv:830-tubdok-5126},
institution = {Hamburg University of Technology},
address = {Hamburg, Germany},
month = oct,
year = 2008,
}

**Abstract**: Recently, Srimani and Xu presented a self-stabilizing algorithm that computes a weakly connected minimal dominating set. They prove an upper bound of O(2^n) until stabilization but they do not provide a lower bound. This paper verifies by giving an example that their algorithm indeed requires O(2^n) moves on a certain graph.