Skip to main content
SpringerLink
Log in

Local Algorithms: Self-stabilization on Speed

  • Conference paper
Book cover Stabilization, Safety, and Security of Distributed Systems (SSS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5873))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dijkstra, E.W.: Self-stabilization in spite of distributed control. Manuscript EWD391 (October 1973)

    Google Scholar 

  2. Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)

    Article  MATH  Google Scholar 

  3. Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing 15(4), 1036–1053 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cole, R., Vishkin, U.: Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control 70(1), 32–53 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  5. Linial, N.: Locality in distributed graph algorithms. SIAM Journal on Computing 21(1), 193–201 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Naor, M., Stockmeyer, L.: What can be computed locally? SIAM Journal on Computing 24(6), 1259–1277 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. 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)

    Google Scholar 

  8. 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)

    Google Scholar 

  9. 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)

    Chapter  Google Scholar 

  10. Awerbuch, B.: Complexity of network synchronization. Journal of the ACM 32(4), 804–823 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  11. Suomela, J.: Survey of local algorithms (manuscript, 2009)

    Google Scholar 

  12. Goldberg, A.V., Plotkin, S.A.: Parallel (Δ + 1)-coloring of constant-degree graphs. Information Processing Letters 25(4), 241–245 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Peleg, D.: Distributed Computing – A Locality-Sensitive Approach. SIAM, Philadelphia (2000)

    MATH  Google Scholar 

  14. 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)

    Google Scholar 

  15. Schneider, M.: Self-stabilization. ACM Computing Surveys 25(1), 45–67 (1993)

    Article  Google Scholar 

  16. Dolev, S.: Self-Stabilization. The MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  17. 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)

    Google Scholar 

  18. 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)

    Chapter  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. 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)

    Google Scholar 

  21. 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)

    Google Scholar 

  22. 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)

    Article  MATH  MathSciNet  Google Scholar 

  23. 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)

    Google Scholar 

  24. 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)

    Chapter  Google Scholar 

  25. 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)

    Google Scholar 

  26. Panconesi, A., Rizzi, R.: Some simple distributed algorithms for sparse networks. Distributed Computing 14(2), 97–100 (2001)

    Article  Google Scholar 

  27. Hańćkowiak, M., Karoński, M., Panconesi, A.: On the distributed complexity of computing maximal matchings. SIAM Journal on Discrete Mathematics 15(1), 41–57 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  28. 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)

    Article  MATH  MathSciNet  Google Scholar 

  29. Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Information Processing Letters 22(2), 77–80 (1986)

    Article  MathSciNet  Google Scholar 

  30. 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)

    Google Scholar 

  31. Kutten, S., Peleg, D.: Tight fault locality. SIAM Journal on Computing 30(1), 247–268 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  32. 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)

    Google Scholar 

  33. 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)

    Chapter  Google Scholar 

  34. Kuhn, F., Wattenhofer, R.: Constant-time distributed dominating set approximation. Distributed Computing 17(4), 303–310 (2005)

    Article  Google Scholar 

  35. 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)

    Chapter  Google Scholar 

  36. 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)

    Google Scholar 

  37. 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)

    Google Scholar 

  38. 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)

    Chapter  Google Scholar 

  39. 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)

    Google Scholar 

  40. Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications, Inc., Mineola (1998)

    MATH  Google Scholar 

  41. Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)

    Google Scholar 

  42. 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)

    Google Scholar 

  43. Hochbaum, D.S.: Approximation algorithms for the set covering and vertex cover problems. SIAM Journal on Computing 11(3), 555–556 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  44. 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)

    Google Scholar 

  45. 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)

    Chapter  Google Scholar 

  46. Lenzen, C., Wattenhofer, R.: Leveraging Linial’s locality limit. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 394–407. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  47. 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)

    Chapter  Google Scholar 

  48. Elkin, M.: Distributed approximation: a survey. ACM SIGACT News 35(4), 40–57 (2004)

    Article  Google Scholar 

  49. Sterling, A.: Self-assembling systems are distributed systems. Manuscript, arXiv:0907.1072 [cs.DC] (July 2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Engineering and Networks Laboratory TIK, ETH Zurich, 8092, Zurich, Switzerland

    Christoph Lenzen & Roger Wattenhofer

  2. Helsinki Institute for Information Technology HIIT, University of Helsinki, P.O. Box 68, FI-00014, Finland

    Jukka Suomela

Authors
  1. Christoph Lenzen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jukka Suomela
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roger Wattenhofer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ecole Polytechnique Fédérale de Lausanne, CH 1015, Lausanne, Switzerland

    Rachid Guerraoui

  2. LIP, ENS Lyon, 46 allée d’Italie, 69236, Lyon cedex 07, France

    Franck Petit

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-05118-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05117-3

  • Online ISBN: 978-3-642-05118-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation