Abstract
We study distributed linearization or topological sorting in peer-to-peer networks. We define strict and eventual variants of the problem. We consider these problems restricted to existing peer identifiers or without this restriction. None of these variants are solvable in the asynchronous message-passing system model. We define a collection of oracles and prove which oracle combination is necessary to enable a solution for each variant of the linearization problem. We then present a linearization algorithm. We prove that this algorithm and a specific combination of the oracles solves each stated variant of the linearization problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aspnes, J., Shah, G.: Skip graphs. ACM Transactions on Algorithms 3(4), 1–37 (2007)
Awerbuch, B., Scheideler, C.: The hyperring: a low-congestion deterministic data structure for distributed environments. In: SODA 2004: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 318–327. Society for Industrial and Applied Mathematics, Philadelphia (2004)
Cavin, D., Sasson, Y., Schiper, A.: Consensus with unknown participants or fundamental self-organization. In: Nikolaidis, I., Barbeau, M., An, H.-C. (eds.) ADHOC-NOW 2004. LNCS, vol. 3158, pp. 135–148. Springer, Heidelberg (2004)
Chandra, T.D., Hadzilacos, V., Toueg, S.: The weakest failure detector for solving consensus. Journal of ACM 43(4), 685–722 (1996)
Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. Journal of the ACM 43(2), 225–267 (1996)
Cramer, C., Fuhrmann, T.: ISPRP: a message-efficient protocol for initializing structured P2P networks. In: International Performance Computing and Communications Conference (IPCCC), pp. 365–370 (2005)
Dijkstra, E.W.: Self-stabilization in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)
Dubois, S., Tixeuil, S.: A taxonomy of daemons in self-stabilization. Technical Report 1110.0334, ArXiv eprint (October 2011)
Emek, Y., Fraigniaud, P., Korman, A., Kutten, S., Peleg, D.: Notions of connectivity in overlay networks. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 25–35. Springer, Heidelberg (2012)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)
Gall, D., Jacob, R., Richa, A.W., Scheideler, C., Schmid, S., Täubig, H.: Time complexity of distributed topological self-stabilization: The case of graph linearization. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 294–305. Springer, Heidelberg (2010)
Gouda, M.G., McGuire, T.M.: Accelerated heartbeat protocols. In: 18th International Conference on Distributed Computing Systems (ICDCS), pp. 202–209 (May 1998)
Greve, F., Tixeuil, S.: Knowledge connectivity vs. synchrony requirements for fault-tolerant agreement in unknown networks. In: Proceedings of IEEE International Conference on Dependable Systems and networks (DSN), pp. 82–91. IEEE (June 2007)
Harvey, N.J.A., Ian Munro, J.: Deterministic skipnet. Inf. Process. Lett. 90(4), 205–208 (2004)
Malkhi, D., Naor, M., Ratajczak, D.: Viceroy: a scalable and dynamic emulation of the butterfly. In: PODC 2002: Proceedings of the Twenty-first Annual Symposium on Principles of Distributed Computing, pp. 183–192. ACM, New York (2002)
Munro, J.I., Papadakis, T., Sedgewick, R.: Deterministic skip lists. In: SODA 1992: Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algogrithms, pp. 367–375. Society for Industrial and Applied Mathematics, Philadelphia (1992)
Nor, R.M., Nesterenko, M., Scheideler, C.: Corona: A stabilizing deterministic message-passing skip list. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 356–370. Springer, Heidelberg (2011)
Onus, M., Richa, A.W., Scheideler, C.: Linearization: Locally self-stabilizing sorting in graphs. In: ALENEX 2007: Proceedings of the Workshop on Algorithm Engineering and Experiments. SIAM ( January 2007)
Rowstron, A., Druschel, P.: Pastry: Scalable, decentralized object location, and routing for large-scale peer-to-peer systems. In: Guerraoui, R. (ed.) Middleware 2001. LNCS, vol. 2218, pp. 329–350. Springer, Heidelberg (2001)
Stoica, I., Morris, R., Liben-Nowell, D., Karger, D.R., Kaashoek, M.F., Dabek, F., Balakrishnan, H.: Chord: a scalable peer-to-peer lookup protocol for Internet applications. IEEE/ACM Transactions on Networking 11(1), 17–32 (2003)
Tixeuil, S.: Self-stabilizing Algorithms. In: Algorithms and Theory of Computation Handbook, 2nd edn., pp. 26.1–26.45. CRC Press, Taylor & Francis Group (2009); Chapman & Hall/CRC Applied Algorithms and Data Structures
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Nor, R.M., Nesterenko, M., Tixeuil, S. (2013). Linearizing Peer-to-Peer Systems with Oracles. In: Higashino, T., Katayama, Y., Masuzawa, T., Potop-Butucaru, M., Yamashita, M. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2013. Lecture Notes in Computer Science, vol 8255. Springer, Cham. https://doi.org/10.1007/978-3-319-03089-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-03089-0_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03088-3
Online ISBN: 978-3-319-03089-0
eBook Packages: Computer ScienceComputer Science (R0)