Abstract
We present a self-stabilizing algorithm for overlay networks that, for an arbitrary metric given by a distance oracle, constructs the graph representing that metric. The graph representing a metric is the unique minimal undirected graph such that for any pair of nodes the length of a shortest path between the nodes corresponds to the distance between the nodes according to the metric. The algorithm works under both an asynchronous and a synchronous dæmon. In the synchronous case, the algorithm stablizes in time O(n) and it is almost silent in that after stabilization a node sends and receives a constant number of messages per round.
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References
Aggarwal, S., Kutten, S.: Time optimal self-stabilizing spanning tree algorithms. In: Shyamasundar, R.K. (ed.) FSTTCS 1993. LNCS, vol. 761, pp. 400–410. Springer, Heidelberg (1993). doi:10.1007/3-540-57529-4_72
Berns, A., Ghosh, S., Pemmaraju, S.V.: Building self-stabilizing overlay networks with the transitive closure framework. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 62–76. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24550-3_7
Clouser, T., Nesterenko, M., Scheideler, C.: Tiara: a self-stabilizing deterministic skip list and skip graph. Theor. Comput. Sci. 428, 18–35 (2012)
Cramer, C., Fuhrmann, T., Informatik, F.F.: Self-stabilizing ring networks on connected graphs. Technical report (2005)
Gärtner, F.C.: A survey of self-stabilizing spanning-tree construction algorithms. Technical report (2003)
Jacob, R., Richa, A., Scheideler, C., Schmid, S., Täubig, H.: A distributed polylogarithmic time algorithm for self-stabilizing skip graphs. In: Proceedings of the 28th ACM Symposium on Principles of Distributed Computing, pp. 131–140. ACM (2009)
Keil, J.M., Gutwin, C.A.: The Delaunay triangulation closely approximates the complete Euclidean graph. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1989. LNCS, vol. 382, pp. 47–56. Springer, Heidelberg (1989). doi:10.1007/3-540-51542-9_6
Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete euclidean graph. Discrete Comput. Geom. 7(1), 13–28 (1992)
Kniesburges, S., Koutsopoulos, A., Scheideler, C.: Re-chord: a self-stabilizing chord overlay network. Theory Comput. Syst. 55(3), 591–612 (2014)
Onus, M., Richa, A.W., Scheideler, C.: Linearization: Locally self-stabilizing sorting in graphs. In: ALENEX (2007)
Richa, A., Scheideler, C., Stevens, P.: Self-stabilizing de bruijn networks. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 416–430. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24550-3_31
Shaker, A., Reeves, D.S.: Self-stabilizing structured ring topology p2p systems. In: Fifth IEEE International Conference on Peer-to-Peer Computing, P2P, pp. 39–46 (2005)
Acknowledgments
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901) and by the EU within FET project MULTIPLEX under contract no. 317532.
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Gmyr, R., Lefèvre, J., Scheideler, C. (2016). Self-stabilizing Metric Graphs. In: Bonakdarpour, B., Petit, F. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2016. Lecture Notes in Computer Science(), vol 10083. Springer, Cham. https://doi.org/10.1007/978-3-319-49259-9_20
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DOI: https://doi.org/10.1007/978-3-319-49259-9_20
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