Skip to main content
SpringerLink
Log in

Fast and Compact Distributed Verification and Self-stabilization of a DFS Tree

  • Conference paper
Principles of Distributed Systems (OPODIS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8878))

Included in the following conference series:

Abstract

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of O(nlogΔ) bits per node and O(nD) respectively, where Δ is the highest degree of a node, n is the number of nodes and D is the diameter of the network. In contrast, our algorithm has a space complexity of O(logn) bits per node, which is optimal for silent-stabilizing spanning trees and runs in O(n) time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, we also present a (non-silent) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Afek, Y., Kutten, S., Yung, M.: The local detection paradigm and its applications to self-stabilization

    Google Scholar 

  2. Awerbuch, B.: A new distributed depth-first-search algorithm. Information Processing Letters 20(3), 147–150 (1985)

    Article  MATH  Google Scholar 

  3. Awerbuch, B., Varghese, G.: Distributed program checking: A paradigm for building self-stabilizing distributed protocols (extended abstract). In: Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, SFCS, 1991, pp. 258–267. IEEE Computer Society, Washington, DC (1991)

    Google Scholar 

  4. Chlamtac, I., Kutten, S.: Tree-based broadcasting in multihop radio networks. IEEE Transactions on Computers 100(10), 1209–1223 (1987)

    Article  Google Scholar 

  5. Cidon, I.: Yet another distributed depth-first-search algorithm. Inf. Process. Lett. 26(6), 301–305 (1988)

    Article  Google Scholar 

  6. Collin, Z., Dolev, S.: Self-stabilizing depth-first search. Information Processing Letters 49(6), 297–301 (1994)

    Article  MATH  Google Scholar 

  7. Cournier, A., Devismes, S., Petit, F., Villain, V.: Snap-stabilizing depth-first search on arbitrary networks. Comput. J., 268–280 (2006)

    Google Scholar 

  8. Cournier, A., Devismes, S., Villain, V.: A snap-stabilizing DFS with a lower space requirement. In: Tixeuil, S., Herman, T. (eds.) SSS 2005. LNCS, vol. 3764, pp. 33–47. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Datta, A.K., Johnen, C., Petit, F., Villain, V.: Self-stabilizing depth-first token circulation in arbitrary rooted networks. Distrib. Comput. 13(4), 207–218 (2000)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  11. Dolev, S.: Self-stabilization. MIT Press (2000)

    Google Scholar 

  12. Dolev, S., Gouda, M.G., Schneider, M.: Memory requirements for silent stabilization. Acta Informatica 36(6), 447–462 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dolev, S., Israeli, A., Moran, S.: Self-stabilization of dynamic systems assuming only read/write atomicity. Distrib. Comput. 7(1), 3–16 (1993)

    Article  MATH  Google Scholar 

  14. Dolev, S., Israeli, A., Moran, S.: Self-stabilization of dynamic systems assuming only read/write atomicity. Distrib. Comput. 7(1), 3–16 (1993)

    Article  MATH  Google Scholar 

  15. Even, S.: Graph Algorithms. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  16. Göös, M., Suomela Locally, J.: checkable proofs. In: Proceedings of the 30th Annual ACM Symposium on Principles of Distributed Computing, PODC 2011, San Jose, CA, USA, June 6-8, pp. 159–168 (2011)

    Google Scholar 

  17. Huang, S.-T., Chen, N.-S.: Self-stabilizing depth-first token circulation on networks. Distributed Computing 7(1), 61–66 (1993)

    Article  MATH  Google Scholar 

  18. Johnen, C., Alari, G., Beauquier, J., Datta, A.K.: Self-stabilizing depth-first token passing on rooted networks. In: Mavronicolas, M. (ed.) WDAG 1997. LNCS, vol. 1320, pp. 260–274. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  19. Johnen, C., Beauquier, J.: Space-efficient, distributed and self-stabilizing depth-first token circulation. In: In Proceedings of the Second Workshop on Self-Stabilizing Systems, pp. 4–1 (1995)

    Google Scholar 

  20. Katz, S., Perry, K.J.: Self-stabilizing extensions for meassage-passing systems. Distributed Computing 7(1), 17–26 (1993)

    Article  MATH  Google Scholar 

  21. Korman, A., Kutten, S.: Distributed verification of minimum spanning trees. In: Proceedings of the Twenty-fifth Annual ACM Symposium on Principles of Distributed Computing, pp. 26–34. ACM, New York (2006)

    Chapter  Google Scholar 

  22. Korman, A., Kutten, S., Masuzawa, T.: Fast and compact self stabilizing verification, computation, and fault detection of an mst. In: Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2011, pp. 311–320. ACM, New York (2011)

    Chapter  Google Scholar 

  23. Korman, A., Kutten, S., Peleg, D.: Proof labeling schemes. Distributed Computing 22(4), 215–233 (2010)

    Article  MATH  Google Scholar 

  24. Petit, F.: Highly space-efficient self-stabilizing depth-first token circulation for trees. In: Lengauer, C., Griebl, M., Gorlatch, S. (eds.) Euro-Par 1997. LNCS, vol. 1300, pp. 47647–47649. Springer, Heidelberg (1997)

    Google Scholar 

  25. Petit, F.: Fast self-stabilizing depth-first token circulation. In: Datta, A.K., Herman, T. (eds.) WSS 2001. LNCS, vol. 2194, pp. 200–215. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Petit, F., Villain, V.: Color optimal self-stabilizing depth-first token circulation. In: ISPAN, pp. 317–323. IEEE Computer Society (1997)

    Google Scholar 

  27. Petit, F., Villain, V.: Optimality and self-stabilization in rooted tree networks. Parallel Processing Letters 10(01), 3–14 (2000)

    Article  Google Scholar 

  28. Petit, F., Villain, V.: Self-stabilizing depth-first token circulation in asynchronous message-passing systems. Computers and Artificial Intelligence 19(5) (2000)

    Google Scholar 

  29. Petit, F., Villain, V.: Optimal snap-stabilizing depth-first token circulation in tree networks. Journal of Parallel and Distributed Computing 67(1), 1–12 (2007)

    Article  MATH  Google Scholar 

  30. Stomp, F.A.: Structured design of self-stabilizing programs. In: Proceedings of the 2nd Israel Symposium on the Theory and Computing Systems, pp. 167–176 (June 1993)

    Google Scholar 

  31. Varghese, G., Jayaram, M.: The fault span of crash failures. Journal of the ACM 47(2), 244–293 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion, Haifa, Israel

    Shay Kutten & Chhaya Trehan

Authors
  1. Shay Kutten
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chhaya Trehan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Microsoft Research Silicon Valley, Mountain View, CA, USA

    Marcos K. Aguilera

  2. DIAG, Sapienza University of Rome, Via Ariosto 25, 00185, Roma, Italy

    Leonardo Querzoni

  3. UPMC Univ Paris 06, LIP6, Inria Paris-Rocquencourt and Sorbonne Universités, 4 place Jussieu, 75005, Paris, France

    Marc Shapiro

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Kutten, S., Trehan, C. (2014). Fast and Compact Distributed Verification and Self-stabilization of a DFS Tree. In: Aguilera, M.K., Querzoni, L., Shapiro, M. (eds) Principles of Distributed Systems. OPODIS 2014. Lecture Notes in Computer Science, vol 8878. Springer, Cham. https://doi.org/10.1007/978-3-319-14472-6_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-14472-6_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14471-9

  • Online ISBN: 978-3-319-14472-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation