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Time Complexity of Distributed Topological Self-Stabilization: The Case of Graph Linearization
Citation key GJRSST-TCDTSSCGL-10
Author Gall, Dominik and Jacob, Riko and Richa, Andréa and Scheideler, Christian and Schmid, Stefan and Täubig, Hanjo
Title of Book Proceedings of 9th Latin American Theoretical Informatics Symposium (LATIN '10)
Pages 294–305
Year 2010
ISBN 978-3-642-12199-9
ISSN 0302-9743
DOI http://dx.doi.org/10.1007/978-3-642-12200-2_27
Location Oaxaca, Mexico
Address Berlin / Heidelberg, Germany
Volume 6034
Month April
Publisher Springer
Series Lecture Notes in Computer Science (LNCS)
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.
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