Skip to main content

Recursion in Distributed Computing

  • Conference paper
  • First Online:
Stabilization, Safety, and Security of Distributed Systems (SSS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6366))

Included in the following conference series:

Abstract

The benefits of developing algorithms via recursion are well known. However, little use of recursion has been done in distributed algorithms, in spite of the fact that recursive structuring principles for distributed systems have been advocated since the beginning of the field. We present several distributed algorithms in a recursive form, which makes them easier to understand and analyze. Also, we expose several interesting issues arising in recursive distributed algorithms. Our goal is to promote the use and study of recursion in distributed algorithms.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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 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.

Similar content being viewed by others

References

  1. Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic Snapshots of Shared Memory. J. ACM 40(4), 873–890 (1993)

    Article  Google Scholar 

  2. Afek, Y., Weisberger, E., Weisman, H.: A Completeness Theorem for a Class of Synchronization Objects (Extended Abstract). In: Proc. 12th Annual ACM Symposium on Principles of Distributed Computing (PODC), Ithaca, New York, USA, August 15-18, pp. 159–170 (1993)

    Google Scholar 

  3. Attiya, H., Bar-Noy, A., Dolev, D.: Sharing Memory Robustly in Message-Passing Systems. J. ACM 42(1), 124–142 (1995)

    Article  Google Scholar 

  4. Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an Asynchronous Environment. J. ACM 37(3), 524–548 (1990)

    Article  MathSciNet  Google Scholar 

  5. Bar-Noy, A., Dolev, D., Dwork, C., Strong, H.R.: Shifting Gears. Changing Algorithms on the Fly to Expedite Byzantine Agreement. Inf. Comput. 97(2), 205–233 (1992)

    Article  MathSciNet  Google Scholar 

  6. Borowsky, E., Gafni, E.: Generalized FLP Impossibility Results for t-Resilient Asynchronous Computations. In: Proc. 25th ACM Symposium on the Theory of Computing (STOC), pp. 91–100. ACM Press, New York (1993)

    Google Scholar 

  7. Borowsky, E., Gafni, E.: Immediate Atomic Snapshots and Fast Renaming (Extended Abstract). In: 12th Annual ACM Symposium on Principles of Distributed Computing (PODC), Ithaca, New York, USA, August 15-18, pp. 41–51 (1993)

    Google Scholar 

  8. Borowsky, E., Gafni, E.: A Simple Algorithmically Reasoned Characterization of Wait-Free Computations (Extended Abstract). In: Proc. 16th ACM Symposium on Principles of Distributed Computing (PODC 1997), Santa Barbara, California, USA, August 21-24, pp. 189–198 (1997)

    Google Scholar 

  9. Borowsky, E., Gafni, E., Lynch, N., Rajsbaum, S.: The BG Distributed Simulation Algorithm. Distributed Computing 14(3), 127–146 (2001)

    Article  Google Scholar 

  10. Cañeda, A., Rajsbaum, S.: New combinatorial topology upper and lower bounds for renaming. In: Proceedings of the 27-th Annual ACM Symposium on Principles of Distributed Computing (PODC), Toronto, Canada, August 18-21, pp. 295–304 (2008)

    Google Scholar 

  11. Chou, C.-T., Gafni, E.: Understanding and Verifying Distributed Algorithms Using Stratified Decomposition. In: Proceedings of the Seventh Annual ACM Symposium on Principles of Distributed Computing (PODC), Toronto, Ontario, Canada, August 15-17, pp. 44–65 (1988)

    Google Scholar 

  12. Coan, B.A., Welch, J.L.: Modular Construction of an Efficient 1-Bit Byzantine Agreement Protocol. Mathematical Systems Theory 26(1), 131–154 (1993)

    Article  MathSciNet  Google Scholar 

  13. Dobson, J., Randell, B.: Building Reliable Secure Computing Systems out of Unreliable Insecure Components. In: Proc. IEEE Conference on Security and Privacy, Oakland, USA, pp. 187–193 (1986)

    Google Scholar 

  14. Elrad, T., Francez, N.: Decomposition of Distributed Programs into Communication-Closed Layers. Sci. Comput. Program 2(3), 155–173 (1982)

    Article  Google Scholar 

  15. Fouren, A.: Exponential examples for two renaming algorithms (August 1999), http://www.cs.technion.ac.il/~hagit/publications/expo.ps.gz

  16. Gafni, E.: Round-by-Round Fault Detectors, Unifying Synchrony and Asynchrony (Extendeda Abstract). In: Proc. 17th Annual ACM Symposium on Principles of Distributed Computing (PODC), Puerto Vallarta, Mexico, June 28-July 2, pp. 143–152 (1998)

    Google Scholar 

  17. Gafni, E., Rajsbaum, S., Herlihy, M.: Subconsensus Tasks: Renaming Is Weaker Than Set Agreement. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 329–338. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Gallager, R.G., Humblet, P.A., Spira, P.M.: A Distributed Algorithm for Minimum-Weight Spanning Trees. ACM Trans. Program. Lang. Syst. 5(1), 66–77 (1983)

    Article  Google Scholar 

  19. Herlihy, M., Rajsbaum, S.: The Topology of Shared-Memory Adversaries. In: Annual ACM Symposium on Principles of Distributed Computing, Proceeding of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, Zurich, Switzerland, pp. 105–113 (2010), ISBN: 978-1-60558-888-9

    Google Scholar 

  20. Herlihy, M.P., Shavit, N.: The Topological Structure of Asynchronous Computability. Journal of the ACM 46(6), 858–923 (1999)

    Article  MathSciNet  Google Scholar 

  21. Lamport, L., Shostak, R.E., Pease, M.C.: The Byzantine Generals Problem. ACM Transactions on Programming Languages and Systems 4(3), 382–401 (1982)

    Article  Google Scholar 

  22. Loui, M.C., Abu-Amara, H.H.: Memory requirements for agreement among unreliable asynchronous processes. In: Preparata, F.P. (ed.) Advances in Computing Research, vol. 4, pp. 163–183. JAI Press, Greenwich (1987)

    Google Scholar 

  23. Manber, U.: Introduction to Algorithms: A Creative Approach. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  24. Randell: Brian Recursively structured distributed computing systems. In: Proc. IEEE Symposium on Reliability in Distributed Software and Database Systems, pp. 3–11 (1983)

    Google Scholar 

  25. Rajsbaum, S., Raynal, M., Travers, C.: An impossibility about failure detectors in the iterated immediate snapshot model. Inf. Process. Lett. 108(3), 160–164 (2008)

    Article  MathSciNet  Google Scholar 

  26. Rajsbaum, S., Raynal, M., Travers, C.: The Iterated Restricted Immediate Snapshot Model. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 487–497. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Saks, M., Zaharoglou, F.: Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge. SIAM Journal on Computing 29(5), 1449–1483 (2000)

    Article  MathSciNet  Google Scholar 

  28. Stojmenovic, I.: Recursive algorithms in computer science courses: Fibonacci numbers and binomial coefficients. IEEE Trans. on Education 43(3), 273–276 (2000)

    Article  Google Scholar 

  29. Weisman, H.: Implementing shared memory overwriting objects. Master’s thesis, Tel Aviv University (May 1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gafni, E., Rajsbaum, S. (2010). Recursion in Distributed Computing. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2010. Lecture Notes in Computer Science, vol 6366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16023-3_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16023-3_30

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16022-6

  • Online ISBN: 978-3-642-16023-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics