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.
For a complete technical report, we refer the reader to [8]. Research supported by the DFG project SCHE 1592/1-1, and NSF Award number CCF-0830704.
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References
Aspnes, J., Shah, G.: Skip graphs. In: Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 384–393 (2003)
Blumofe, R.D., Leiserson, C.E.: Space-e cient scheduling of multithreaded computations. SIAM Journal on Computing 27(1), 202–229 (1998)
Blumofe, R.D., Leiserson, C.E.: Scheduling multithreaded computations by work stealing. Journal of the ACM 46(5), 720–748 (1999)
Clouser, T., Nesterenko, M., Scheideler, C.: Tiara: A self-stabilizing deterministic skip list. In: Kulkarni, S., Schiper, A. (eds.) SSS 2008. LNCS, vol. 5340, pp. 124–140. Springer, Heidelberg (2008)
Cramer, C., Fuhrmann, T.: Self-stabilizing ring networks on connected graphs. Technical Report 2005-5, System Architecture Group, University of Karlsruhe (2005)
Dolev, D., Hoch, E.N., van Renesse, R.: Self-stabilizing and byzantine-tolerant overlay network. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 343–357. Springer, Heidelberg (2007)
Dolev, S., Kat, R.I.: Hypertree for self-stabilizing peer-to-peer systems. Distributed Computing 20(5), 375–388 (2008)
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)
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)
Jacob, R., Ritscher, S., Scheideler, C., Schmid, S.: A self-stabilizing and local delaunay graph construction. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878. Springer, Heidelberg (2009)
Kuhn, F., Schmid, S., Wattenhofer, R.: A self-repairing peer-to-peer system resilient to dynamic adversarial churn. In: Castro, M., van Renesse, R. (eds.) IPTPS 2005. LNCS, vol. 3640, pp. 13–23. Springer, Heidelberg (2005)
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)
Scheideler, C., Schmid, S.: A distributed and oblivious heap. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 571–582. Springer, Heidelberg (2009)
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)
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)
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Gall, D., Jacob, R., Richa, A., Scheideler, C., Schmid, S., Täubig, H. (2010). Time Complexity of Distributed Topological Self-stabilization: The Case of Graph Linearization. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_27
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