Abstract
Resource Discovery is a crucial issue in the deployment of computational grids over large scale peer-to-peer platforms. Because they efficiently allow range queries, Tries (a.k.a., Prefix Trees) appear to be among promising ways in the design of distributed data structures indexing resources. Self-stabilization is an efficient approach in the design of reliable solutions for dynamic systems. A snap-stabilizing algorithm guarantees that it always behaves according to its specification. In other words, a snap-stabilizing algorithm is also a self-stabilizing algorithm which stabilizes in 0 steps.
In this paper, we provide the first snap-stabilizing protocol for trie construction. We design particular tries called Proper Greatest Common Prefix (PGCP) Tree. The proposed algorithm arranges the n label values stored in the tree, in average, in O(h + h′) rounds, where h and h′ are the initial and final heights of the tree, respectively. In the worst case, the algorithm requires an O(n) extra space on each node, O(n) rounds and O(n 2) actions. However, simulations show that, using relevant data sets, this worst case is far from being reached and confirm the average complexities, making this algorithm efficient in practice.
This work was developed with financial support from the ANR (Agence Nationale de la Recherche) through the LEGO project referenced ANR-05-CIGC-11.
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References
Andrzejak, A., Xu, Z.: Scalable, Efficient Range Queries for Grid Information Services. In: Peer-to-Peer Computing, pp. 33–40 (2002)
Arora, A., Gouda, M.G.: Distributed Reset. IEEE Transactions on Computers 43, 1026–1038 (1994)
Aspnes, J., Shah, G.: Skip Graphs. In: Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 384–393 (January 2003)
Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: Time Optimal Self-stabilizing Synchronization. In: STOC 1993. Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pp. 652–661. ACM Press, New York (1993)
Balazinska, M., Balakrishnan, H., Karger, D.: INS/Twine: A Scalable Peer-to-Peer Architecture for Intentional Resource Discovery. In: International Conference on Pervasive Computing 2002 (2002)
Basu, S., Banerjee, S., Sharma, P., Lee, S.: NodeWiz: Peer-to-Peer Resource Discovery for Grids. In: GP2PC. 5th International Workshop on Global and Peer-to-Peer Computing (May 2005)
Bein, D., Datta, A.K, Villain, V.: Snap-Stabilizing Optimal Binary Search Tree. In: Tixeuil, S., Herman, T. (eds.) SSS 2005. LNCS, vol. 3764, pp. 1–17. Springer, Heidelberg (2005)
Bui, A., Datta, A., Petit, F., Villain, V.: State-optimal snap-stabilizing pif in tree networks. In: IEEE (ed.) Proceedings of the 4th International Workshop on Self-Stabilizing Systems, pp. 78–85. IEEE Computer Society Press, Los Alamitos (1999)
Cappello, F., et al.: Grid’5000: a Large Scale, Reconfigurable, Controlable and Monitorable Grid Platform. In: Gschwind, T., Aßmann, U., Nierstrasz, O. (eds.) SC 2005. LNCS, vol. 3628, pp. 99–106. Springer, Heidelberg (2005)
Caron, E., Desprez, F., Fourdrignier, C., Petit, F., Tedeschi, C.: A Repair Mechanism for Tree-structured Peer-to-peer Systems. In: Robert, Y., Parashar, M., Badrinath, R., Prasanna, V.K. (eds.) HiPC 2006. LNCS, vol. 4297, Springer, Heidelberg (2006)
Caron, E., Desprez, F., Tedeschi, C.: A Dynamic Prefix Tree for the Service Discovery Within Large Scale Grids. In: Montresor, A., Wierzbicki, A., Shahmehri, N. (eds.) P2P2006. The Sixth IEEE International Conference on Peer-to-Peer Computing, Cambridge, September 6-8 2006, pp. 106–113. IEEE Computer Society Press, Los Alamitos (2006)
Chen, N.S., Yu, H.P., Huang, S.T.: A Self-stabilizing Algorithm for Constructing Spanning Trees. Information Processing Letters 39, 147–151 (1991)
Cournier, A., Datta, A.K., Petit, F., Villain, V.: Enabling Snap-Stabilization. In: ICDCS 2003. Proceedings of the 23rd International Conference on Distributed Computing Systems, p. 12. IEEE Computer Society Press, Washington (2003)
Datta, A., Hauswirth, M., John, R., Schmidt, R., Aberer, K.: Range Queries in Trie-Structured Overlays. In: The Fifth IEEE International Conference on Peer-to-Peer Computing (2005)
Dijkstra, E.W.: Self-stabilizing Systems in Spite of Distributed Control. Commun. ACM 17(11), 643–644 (1974)
Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)
Dolev, S., Israeli, A., Moran, S.: Self-stabilization of Dynamic Systems Assuming only Read/Write Atomicity. Distributed Computing 7, 3–16 (1993)
Herault, T., Lemarinier, P., Peres, O., Pilard, L., Beauquier, J.: A model for large scale self-stabilization. In: I E E E Sc. (ed.) IPDPS 2007. 21th International Parallel and Distributed Processing Symposium, IEEE Computer Society Press, Los Alamitos (2007)
Herman, T., Pirwani, I.: A Composite Stabilizing Data Structure. In: Datta, A.K., Herman, T. (eds.) WSS 2001. LNCS, vol. 2194, pp. 182–197. Springer, Heidelberg (2001)
Herman, T., Masuzawa, T.: A Stabilizing Search Tree with Availability Properties. In: IEEE (ed.) ISADS 2001. Proceedings of the 5th International Symposium on Autonomous Decentralized Systems, pp. 398–405 (2001)
Herman, T., Masuzawa, T.: Available Stabilzing Heaps. Information Processing Letters 77, 115–121 (2001)
Iamnitchi, A., Foster, I.: On Death, Taxes, and the Convergence of Peer-to-Peer and Grid Computing. In: Kaashoek, M.F., Stoica, I. (eds.) IPTPS 2003. LNCS, vol. 2735, pp. 118–128. Springer, Heidelberg (2003)
Oppenheimer, D., Albrecht, J., Patterson, D., Vahdat, A.: Distributed Resource Discovery on PlanetLab with SWORD. In: WORLDS. Proceedings of the ACM/USENIX Workshop on Real, Large Distributed Systems (December 2004)
Ramabhadran, S., Ratnasamy, S., Hellerstein, J.M., Shenker, S.: Prefix Hash Tree An indexing Data Structure over Distributed Hash Tables. In: Proceedings of the 23rd ACM Symposium on Principles of Distributed Computing, St. John’s, Newfoundland, Canada (July 2004)
Ratnasamy, S., Francis, P., Handley, M., Karp, R., Shenker, S.: A Scalable Content-Adressable Network. In: ACM SIGCOMM, ACM Press, New York (2001)
Rowstron, A., Druschel, P.: Pastry: Scalable, Distributed 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)
Schmidt, C., Parashar, M.: Enabling Flexible Queries with Guarantees in P2P Systems. IEEE Internet Computing 8(3), 19–26 (2004)
Shu, Y., Ooi, B.C., Tan, K., Zhou, A.: Supporting Multi-Dimensional Range Queries in Peer-to-Peer Systems. In: Peer-to-Peer Computing, pp. 173–180 (2005)
Stoica, I., Morris, R., Karger, D., Kaashoek, M., Balakrishnan, H.: Chord: A Scalable Peer-to-Peer Lookup service for Internet Applications. In: ACM SIGCOMM, pp. 149–160. ACM Press, New York (2001)
Triantafillou, P., Pitoura, T.: Towards a Unifying Framework for Complex Query Processing over Structured Peer-to-Peer Data Networks. In: Aberer, K., Koubarakis, M., Kalogeraki, V. (eds.) DBISP2P 2003. LNCS, vol. 2944, pp. 169–183. Springer, Heidelberg (2004)
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Caron, E., Desprez, F., Petit, F., Tedeschi, C. (2007). Snap-Stabilizing Prefix Tree for Peer-to-Peer Systems. In: Masuzawa, T., Tixeuil, S. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2007. Lecture Notes in Computer Science, vol 4838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76627-8_9
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