Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Reducing the Number of Messages in Self-stabilizing Protocols

  • Conference paper
  • First Online:
Stabilization, Safety, and Security of Distributed Systems (SSS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11914))

  • 472 Accesses

Abstract

Self-stabilizing algorithms recover from sever faults, such as inconsistent initialization. Traditionally, when designing a self-stabilizing message-passing algorithm, the main goal was to reduce the time until stabilization. The message cost was neglected. In this work, we strive to reduce the number of messages sent on the average per time period. As a tool, we present a stabilizing module that can message-efficiently determine when a task (from a wide family of tasks) is terminated. False positive detection is possible, but only when faults occurred. This module can then be used in the transformation of non self-stabilizing algorithms into self-stabilizing ones.

This study has been partially supported by the anr project Estate (ANR-16-CE25-0009).

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Notes

  1. 1.

    A proof labeling scheme has to be designed especially for \(\mathcal {A}\), and some changes to \(\mathcal {A}\) may be needed in order to generate the specific “label” for the proof labeling scheme.

  2. 2.

    A snap-stabilizing [7] algorithm is a self-stabilizing algorithm that recovers immediately after faults occurred.

  3. 3.

    Predicate \(Quiet(p)\) is defined in Sect. 2.

References

  1. Afek, Y., Kutten, S., Yung, M.: The local detection paradigm and its application to self-stabilization. Theor. Comput. Sci. 186(1–2), 199–229 (1997)

    Article  MathSciNet  Google Scholar 

  2. Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: Time optimal self-stabilizing synchronization. In: STOC 1993, pp. 652–661 (1993)

    Google Scholar 

  3. Awerbuch, B., Patt-Shamir, B., Varghese, G.: Self-stabilization by local checking and correction (extended abstract). In: FOCS 1991, pp. 268–277 (1991)

    Google Scholar 

  4. Awerbuch, B., Patt-Shamir, B., Varghese, G., Dolev, S.: Self-stabilization by local checking and global reset. In: WDAG 1994, pp. 326–339 (1994)

    Chapter  Google Scholar 

  5. Awerbuch, B., Varghese, G.: Distributed program checking: a paradigm for building self-stabilizing distributed protocols. In: FOCS 1991, pp. 258–267 (1991)

    Google Scholar 

  6. Boulinier, C., Petit, F., Villain, V.: When graph theory helps self-stabilization. In: PODC 2004, pp. 150–159 (2004)

    Google Scholar 

  7. Bui, A., Datta, A.K., Petit, F., Villain, V.: State-optimal snap-stabilizing PIF in tree networks. In: WSS 1999, pp. 78–85 (1999)

    Google Scholar 

  8. Chandy, K.M., Misra, J.: An example of stepwise refinement of distributed programs: quiescence detection. ACM TOPLAS 8(3), 326–343 (1986)

    Article  Google Scholar 

  9. Cournier, A., Datta, A.K., Devismes, S., Petit, F., Villain, V.: The expressive power of snap-stabilization. Theor. Comput. Sci. 626, 40–66 (2016)

    Article  MathSciNet  Google Scholar 

  10. Delaët, S., Devismes, S., Nesterenko, M., Tixeuil, S.: Snap-stabilization in message-passing systems. J. Parallel Distrib. Comput. 70(12), 1220–1230 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Dijkstra, E.W., Scholten, C.S.: Termination detection for diffusing computations. Inf. Process. Lett. 11(1), 1–4 (1980)

    Article  MathSciNet  Google Scholar 

  13. Dolev, S.: Self-stabilization. MIT press, Cambridge (2000)

    Book  Google Scholar 

  14. Francez, N.: Distributed termination. ACM TOPLAS 2(1), 42–55 (1980)

    Article  MathSciNet  Google Scholar 

  15. Francez, N., Rodeh, M., Sintzoff, M.: Distributed termination with interval assertions. In: Díaz, J., Ramos, I. (eds.) ICFPC 1981. LNCS, vol. 107, pp. 280–291. Springer, Heidelberg (1981). https://doi.org/10.1007/3-540-10699-5_105

    Chapter  Google Scholar 

  16. Hendler, D., Kutten, S.: Bounded-wait combining: constructing robust and high-throughput shared objects. Distrib. Comput. 21(6), 405–431 (2009)

    Article  Google Scholar 

  17. Katz, S., Perry, K.J.: Self-stabilizing extensions for message-passing systems. Distrib. Comput. 7(1), 17–26 (1993)

    Article  Google Scholar 

  18. Korman, A., Kutten, S., Masuzawa, T.: Fast and compact self-stabilizing verification, computation, and fault detection of an MST. In: PODC 2011, pp. 311–320 (2011)

    Google Scholar 

  19. Korman, A., Kutten, S., Peleg, D.: Proof labeling schemes. Distrib. Comput. 22(4), 215–233 (2010)

    Article  Google Scholar 

  20. Levé, F., Mohamed, K., Villain, V.: Snap-stabilizing PIF on arbitrary connected networks in message passing model. In: SSS 2016, pp. 281–297 (2016)

    Google Scholar 

  21. Matocha, J., Camp, T.: A taxonomy of distributed termination detection algorithms. J. Syst. Softw. 43(3), 207–221 (1998)

    Article  Google Scholar 

  22. Varghese, G.: Self-stabilization by counter flushing. SIAM J. Comput. 30(2), 486–510 (2000)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sorbonne Université, CNRS, LIP6, 75005, Paris, France

    Anaïs Durand

  2. Technion - Israel Institute of Technology, Haifa, Israel

    Shay Kutten

Authors
  1. Anaïs Durand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shay Kutten
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anaïs Durand .

Editor information

Editors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Mohsen Ghaffari

  2. Kent State University, Kent, OH, USA

    Mikhail Nesterenko

  3. Sorbonne University, Paris, France

    Sébastien Tixeuil

  4. CEA LIST, Gif-sur-Yvette, France

    Sara Tucci

  5. Kyushu University, Fukuoka, Japan

    Yukiko Yamauchi

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

Durand, A., Kutten, S. (2019). Reducing the Number of Messages in Self-stabilizing Protocols. In: Ghaffari, M., Nesterenko, M., Tixeuil, S., Tucci, S., Yamauchi, Y. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2019. Lecture Notes in Computer Science(), vol 11914. Springer, Cham. https://doi.org/10.1007/978-3-030-34992-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34992-9_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34991-2

  • Online ISBN: 978-3-030-34992-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation