Time Complexity of Distributed Topological Self-stabilization: The Case of Graph Linearization
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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- 1.Aspnes, J., Shah, G.: Skip graphs. In: Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 384–393 (2003)Google Scholar
- 5.Cramer, C., Fuhrmann, T.: Self-stabilizing ring networks on connected graphs. Technical Report 2005-5, System Architecture Group, University of Karlsruhe (2005)Google Scholar
- 8.Gall, D., Jacob, R., Richa, A., Scheideler, C., Schmid, S., Täubig, H.: Modeling scalability in distributed self-stabilization: The case of graph linearization. Technical Report TUM-I0835, Technische Universität München, Computer Science Dept. (November 2008)Google Scholar
- 9.Jacob, R., Richa, A., Scheideler, C., Schmid, S., Täubig, H.: A distributed polylogarithmic time algorithm for self-stabilizing skip graphs. In: Proc. ACM Symp. on Principles of Distributed Computing, PODC (2009)Google Scholar
- 12.Onus, M., Richa, A., Scheideler, C.: Linearization: Locally self-stabilizing sorting in graphs. In: Proc. 9th Workshop on Algorithm Engineering and Experiments (ALENEX). SIAM, Philadelphia (2007)Google Scholar
- 14.Shaker, A., Reeves, D.S.: Self-stabilizing structured ring topology P2P systems. In: Proc. 5th IEEE International Conference on Peer-to-Peer Computing, pp. 39–46 (2005)Google Scholar
- 15.Stoica, I., Morris, R., Karger, D., Kaashoek, M.F., Balakrishnan, H.: Chord: A scalable peer-to-peer lookup service for internet applications. Technical Report MIT-LCS-TR-819. MIT (2001)Google Scholar