Skip to main content
SpringerLink
Log in

Making Randomized Algorithms Self-stabilizing

  • Conference paper
  • First Online:
Book cover Structural Information and Communication Complexity (SIROCCO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11639))

Abstract

It is well known that the areas of self-stabilizing algorithms and local algorithms are closely related. Using program transformation techniques local algorithms can be made self-stabilizing, albeit an increase in run-time or memory consumption is often unavoidable. Unfortunately these techniques often do not apply to randomized algorithms, which are often simpler and faster than deterministic algorithms. In this paper we demonstrate that it is possible to take over ideas from randomized distributed algorithms to self-stabilizing algorithms. We present two simple self-stabilizing algorithms computing a maximal independent set and a maximal matching and terminate in the synchronous model with high probability in \(O(\log n)\) rounds. The algorithms outperform all existing algorithms that do not rely on unique identifiers.

This work is supported by the Deutsche Forschungsgemeinschaft (DFG) under grant DFG TU 221/6-3.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Afek, Y., Kutten, S., Yung, M.: The local detection paradigm and its applications to self-stabilization. Theor. Comput. Sci. 186(1), 199–229 (1997)

    Article  MathSciNet  Google Scholar 

  2. Alon, N., Babai, L., Itai, A.: A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms 7(4), 567–583 (1986)

    Article  MathSciNet  Google Scholar 

  3. Awerbuch, B., Varghese, G.: Distributed program checking: a paradigm for building self-stabilizing distributed protocols. In: Proceedings of 32nd Annual Symposium of Foundations of Computer Science, pp. 258–267, October 1991

    Google Scholar 

  4. Awerbuch, B., Patt-Shamir, B., Varghese, G., Dolev, S.: Self-stabilization by local checking and global reset. In: Tel, G., Vitányi, P. (eds.) WDAG 1994. LNCS, vol. 857, pp. 326–339. Springer, Heidelberg (1994). https://doi.org/10.1007/BFb0020443

    Chapter  Google Scholar 

  5. Barenboim, L., Elkin, M., Goldenberg, U.: Locally-iterative distributed \((\varDelta +1)\)-Coloring below szegedy-vishwanathan barrier, and applications to self-stabilization and to restricted-bandwidth models. In: Proceedings of ACM Symposium on Principles of Distributed Computing, pp. 437–446 (2018)

    Google Scholar 

  6. Barenboim, L., Elkin, M., Pettie, S., Schneider, J.: The locality of distributed symmetry breaking. J. ACM 63(3), 20:1–20:45 (2016)

    Article  MathSciNet  Google Scholar 

  7. Boulinier, C., Petit, F., Villain, V.: Synchronous vs. Asynchronous Unison. In: Tixeuil, S., Herman, T. (eds.) SSS 2005. LNCS, vol. 3764, pp. 18–32. Springer, Heidelberg (2005). https://doi.org/10.1007/11577327_2

    Chapter  Google Scholar 

  8. Cohen, J., Lefevre, J., Maamra, K., Pilard, L., Sohier, D.: A self-stabilizing algorithm for maximal matching in anonymous networks. PPL 26(04), 1650016 (2016)

    MathSciNet  MATH  Google Scholar 

  9. Devismes, S., Tixeuil, S., Yamashita, M.: Weak vs. self vs. probabilistic stabilization. Int. J. Found. Comput. Sci. 26(3), 291–319 (2015)

    Article  MathSciNet  Google Scholar 

  10. Dolev, S., Israeli, A., Moran, S.: Analyzing expected time by scheduler-luck games. IEEE Trans. Softw. Eng. 21(5), 429–439 (1995)

    Article  Google Scholar 

  11. Fischer, M.: Improved deterministic distributed matching via rounding. In: Richa, A. (ed.) Distributed Computing, vol. 91, pp. 17:1–17:15. Springer, Heidelberg (2017). https://doi.org/10.1007/s00446-018-0344-4

    Chapter  Google Scholar 

  12. Ghaffari, M.: An improved distributed algorithm for maximal independent set. In: Proceedings of 27th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 270–277 (2016)

    Google Scholar 

  13. Guellati, N., Kheddouci, H.: A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. J. Parallel Distrib. Comput. 70(4), 406–415 (2010)

    Article  Google Scholar 

  14. Herman, T.: Probabilistic self-stabilization. IPL 35(2), 63–67 (1990)

    Article  MathSciNet  Google Scholar 

  15. Herman, T., Ghosh, S.: Stabilizing phase-clocks. IPL 54(5), 259–265 (1995)

    Article  Google Scholar 

  16. Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. IPL 22(2), 77–80 (1986)

    Article  MathSciNet  Google Scholar 

  17. Kravchik, A., Kutten, S.: Time optimal synchronous self stabilizing spanning tree. In: Afek, Y. (ed.) DISC 2013. LNCS, vol. 8205, pp. 91–105. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41527-2_7

    Chapter  Google Scholar 

  18. Lenzen, C., Suomela, J., Wattenhofer, R.: Local algorithms: self-stabilization on speed. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 17–34. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05118-0_2

    Chapter  Google Scholar 

  19. Lotker, Z., Patt-Shamir, B., Pettie, S.: Improved distributed approximate matching. J. ACM 62(5), 38:1–38:17 (2015)

    Article  MathSciNet  Google Scholar 

  20. Métivier, Y., Robson, J.M., Saheb-Djahromi, N., Zemmari, A.: An optimal bit complexity randomized distributed MIS algorithm. Distrib. Comput. 23(5), 331–340 (2011)

    Article  Google Scholar 

  21. Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM Society for Industrial and Applied Mathematics, Philadelphia (2000)

    Book  Google Scholar 

  22. Turau, V.: Computing fault-containment times of self-stabilizing algorithms using lumped Markov chains. Algorithms 11(5), 58 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Telematics, Hamburg University of Technology, Hamburg, Germany

    Volker Turau

Authors
  1. Volker Turau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Volker Turau .

Editor information

Editors and Affiliations

  1. Technion, Haifa, Israel

    Keren Censor-Hillel

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Turau, V. (2019). Making Randomized Algorithms Self-stabilizing. In: Censor-Hillel, K., Flammini, M. (eds) Structural Information and Communication Complexity. SIROCCO 2019. Lecture Notes in Computer Science(), vol 11639. Springer, Cham. https://doi.org/10.1007/978-3-030-24922-9_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-24922-9_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24921-2

  • Online ISBN: 978-3-030-24922-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation