Abstract
Fault tolerance is one of the main concepts in distributed computing. It has been tackled from different angles, e.g. by building replicated systems that can survive crash failures of individual components, or even systems that can tolerate a minority of arbitrarily malicious (“Byzantine”) participants.
Self-stabilization, a fault tolerance concept coined by the late Edsger W. Dijkstra in 1973 [1,2], is of a different stamp. A self-stabilizing system must survive arbitrary failures, beyond Byzantine failures, including for instance a total wipe out of volatile memory at all nodes. In other words, the system must self-heal and converge to a correct state even if starting in an arbitrary state, provided that no further faults happen.
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Dijkstra, E.W.: Self-stabilization in spite of distributed control. Manuscript EWD391 (October 1973)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)
Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing 15(4), 1036–1053 (1986)
Cole, R., Vishkin, U.: Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control 70(1), 32–53 (1986)
Linial, N.: Locality in distributed graph algorithms. SIAM Journal on Computing 21(1), 193–201 (1992)
Naor, M., Stockmeyer, L.: What can be computed locally? SIAM Journal on Computing 24(6), 1259–1277 (1995)
Suomela, J.: Optimisation Problems in Wireless Sensor Networks: Local Algorithms and Local Graphs. PhD thesis, University of Helsinki, Department of Computer Science, Helsinki, Finland (May 2009)
Awerbuch, B., Sipser, M.: Dynamic networks are as fast as static networks. In: Proc. 29th Symposium on Foundations of Computer Science (FOCS), pp. 206–219. IEEE, Los Alamitos (1988)
Awerbuch, B., Varghese, G.: Distributed program checking: a paradigm for building self-stabilizing distributed protocols. In: Proc. 32nd Symposium on Foundations of Computer Science (FOCS), pp. 258–267. IEEE, Los Alamitos (1991)
Awerbuch, B.: Complexity of network synchronization. Journal of the ACM 32(4), 804–823 (1985)
Suomela, J.: Survey of local algorithms (manuscript, 2009)
Goldberg, A.V., Plotkin, S.A.: Parallel (Δ + 1)-coloring of constant-degree graphs. Information Processing Letters 25(4), 241–245 (1987)
Peleg, D.: Distributed Computing – A Locality-Sensitive Approach. SIAM, Philadelphia (2000)
Schneider, J., Wattenhofer, R.: A log-star distributed maximal independent set algorithm for growth-bounded graphs. In: Proc. 27th Symposium on Principles of Distributed Computing (PODC), pp. 35–44. ACM Press, New York (2008)
Schneider, M.: Self-stabilization. ACM Computing Surveys 25(1), 45–67 (1993)
Dolev, S.: Self-Stabilization. The MIT Press, Cambridge (2000)
Kothapalli, K., Scheideler, C., Onus, M., Schindelhauer, C.: Distributed coloring in \(\tilde{O}(\sqrt{\log n})\) bit rounds. In: Proc. 20th International Parallel and Distributed Processing Symposium (IPDPS). IEEE, Los Alamitos (2006)
Awerbuch, B., Patt-Shamir, B., Varghese, G.: Self-stabilization by local checking and correction. In: Proc. 32nd Symposium on Foundations of Computer Science (FOCS), pp. 268–277. IEEE, Los Alamitos (1991)
Mayer, A., Naor, M., Stockmeryer, L.: Local computations on static and dynamic graphs. In: Proc. 3rd Israel Symposium on the Theory of Computing and Systems (ISTCS), pp. 268–278. IEEE, Los Alamitos (1995)
Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: Time optimal self-stabilizing synchronization. In: Proc. 25th Symposium on Theory of Computing (STOC), pp. 652–661. ACM Press, New York (1993)
Angluin, D.: Local and global properties in networks of processors. In: Proc. 12th Symposium on Theory of Computing (STOC), pp. 82–93. ACM Press, New York (1980)
Goldberg, A.V., Plotkin, S.A., Shannon, G.E.: Parallel symmetry-breaking in sparse graphs. SIAM Journal on Discrete Mathematics 1(4), 434–446 (1988)
Kuhn, F., Wattenhofer, R.: On the complexity of distributed graph coloring. In: Proc. 25th Symposium on Principles of Distributed Computing (PODC), pp. 7–15. ACM Press, New York (2006)
Barenboim, L., Elkin, M.: Distributed (Δ + 1)-coloring in linear (in Δ) time. In: Proc. 41st Symposium on Theory of Computing (STOC), pp. 111–120. ACM Press, New York (2009)
Kuhn, F.: Weak graph colorings: Distributed algorithms and applications. In: Proc. 21st Symposium on Parallelism in Algorithms and Architectures (SPAA). ACM Press, New York (to appear, 2009)
Panconesi, A., Rizzi, R.: Some simple distributed algorithms for sparse networks. Distributed Computing 14(2), 97–100 (2001)
Hańćkowiak, M., Karoński, M., Panconesi, A.: On the distributed complexity of computing maximal matchings. SIAM Journal on Discrete Mathematics 15(1), 41–57 (2001)
Alon, N., Babai, L., Itai, A.: A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms 7(4), 567–583 (1986)
Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Information Processing Letters 22(2), 77–80 (1986)
Métivier, Y., Robson, J.M., Nasser, S.D., Zemmari, A.: An optimal bit complexity randomised distributed MIS algorithm. In: SIROCCO 2009. LNCS, vol. 5869. Springer, Heidelberg (to appear, 2009)
Kutten, S., Peleg, D.: Tight fault locality. SIAM Journal on Computing 30(1), 247–268 (2000)
Papadimitriou, C.H., Yannakakis, M.: Linear programming without the matrix. In: Proc. 25th Symposium on Theory of Computing (STOC), pp. 121–129. ACM Press, New York (1993)
Bartal, Y., Byers, J.W., Raz, D.: Global optimization using local information with applications to flow control. In: Proc. 38th Symposium on Foundations of Computer Science (FOCS), pp. 303–312. IEEE Computer Society Press, Los Alamitos (1997)
Kuhn, F., Wattenhofer, R.: Constant-time distributed dominating set approximation. Distributed Computing 17(4), 303–310 (2005)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: The price of being near-sighted. In: Proc. 17th Symposium on Discrete Algorithms (SODA), pp. 980–989. ACM Press, New York (2006)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: What cannot be computed locally! In: Proc. 23rd Symposium on Principles of Distributed Computing (PODC), pp. 300–309. ACM Press, New York (2004)
Floréen, P., Kaasinen, J., Kaski, P., Suomela, J.: An optimal local approximation algorithm for max-min linear programs. In: Proc. 21st Symposium on Parallelism in Algorithms and Architectures (SPAA). ACM Press, New York (to appear, 2009)
Floréen, P., Hassinen, M., Kaski, P., Suomela, J.: Tight local approximation results for max-min linear programs. In: Fekete, S.P. (ed.) ALGOSENSORS 2008. LNCS, vol. 5389, pp. 2–17. Springer, Heidelberg (2008)
Floréen, P., Kaski, P., Musto, T., Suomela, J.: Approximating max-min linear programs with local algorithms. In: Proc. 22nd International Parallel and Distributed Processing Symposium (IPDPS). IEEE, Los Alamitos (2008)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications, Inc., Mineola (1998)
Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: Fault-tolerant clustering in ad hoc and sensor networks. In: Proc. 26th International Conference on Distributed Computing Systems (ICDCS). IEEE Computer Society Press, Los Alamitos (2006)
Hochbaum, D.S.: Approximation algorithms for the set covering and vertex cover problems. SIAM Journal on Computing 11(3), 555–556 (1982)
Åstrand, M., Floréen, P., Polishchuk, V., Rybicki, J., Suomela, J., Uitto, J.: A local 2-approximation algorithm for the vertex cover problem. In: Proc. 23rd Symposium on Distributed Computing (DISC). Springer, Heidelberg (to appear, 2009)
Czygrinow, A., Hańćkowiak, M., Wawrzyniak, W.: Fast distributed approximations in planar graphs. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 78–92. Springer, Heidelberg (2008)
Lenzen, C., Wattenhofer, R.: Leveraging Linial’s locality limit. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 394–407. Springer, Heidelberg (2008)
Lenzen, C., Oswald, Y.A., Wattenhofer, R.: What can be approximated locally? In: Proc. 20th Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 46–54. ACM Press, New York (2008)
Elkin, M.: Distributed approximation: a survey. ACM SIGACT News 35(4), 40–57 (2004)
Sterling, A.: Self-assembling systems are distributed systems. Manuscript, arXiv:0907.1072 [cs.DC] (July 2009)
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Lenzen, C., Suomela, J., Wattenhofer, R. (2009). Local Algorithms: Self-stabilization on Speed. In: Guerraoui, R., Petit, F. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2009. Lecture Notes in Computer Science, vol 5873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05118-0_2
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DOI: https://doi.org/10.1007/978-3-642-05118-0_2
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