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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-49259-9_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49258-2
Online ISBN: 978-3-319-49259-9
eBook Packages: Computer ScienceComputer Science (R0)