Skip to main content
SpringerLink
Log in

Maximum Metric Spanning Tree Made Byzantine Tolerant

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. This paper focuses on systems that are both self-stabilizing and Byzantine tolerant. Combining these two properties is known to induce many impossibility results. Hence, there exist several fault tolerance schemes to contain Byzantine faults in self-stabilization. In this paper, we consider the well known problem of constructing a maximum metric tree in this context. We provide a new distributed protocol that ensures the best possible containment with respect to topology-aware strict and strong stabilization.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Afek, Y., Kutten, S., Yung, M.: Memory-efficient self stabilizing protocols for general networks. In: 4th International Workshop on Distributed Algorithms (WDAG 1990), pp. 15–28 (1990)

  2. Blin, L., Butelle, F.: The first approximated distributed algorithm for the minimum degree spanning tree problem on general graphs. Int. J. Found. Comput. Sci. 15(3), 507–516 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Blin, L., Potop-Butucaru, M., Rovedakis, S.: A superstabilizing log( )-approximation algorithm for dynamic steiner trees. In: 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2009), pp. 133–148 (2009)

  4. Blin, L., Potop-Butucaru, M., Rovedakis, S.: Self-stabilizing minimum degree spanning tree within one from the optimal degree. J. Parallel Distrib. Comput. 71(3), 438–449 (2011)

    Article  MATH  Google Scholar 

  5. Burman, J., Kutten, S.: Time optimal asynchronous self-stabilizing spanning tree. In: 21st International Symposium on Distributed Computing (DISC 2007), pp. 92–107 (2007)

  6. Butelle, F., Lavault, C., Bui, M.: A uniform self-stabilizing minimum diameter tree algorithm (extended abstract). In: 9th International Workshop on Distributed Algorithms (WDAG 1995), pp. 257–272 (1995)

  7. Chen, G.H., Houle, M.E., Kuo, M.T.: The steiner problem in distributed computing systems. Inf. Sci. 74(1–2), 73–96 (1993)

    MATH  MathSciNet  Google Scholar 

  8. Collin, Z., Dolev, S.: Self-stabilizing depth-first search. Inf. Process. Lett. 49(6), 297–301 (1994)

    Article  MATH  Google Scholar 

  9. Daliot, A., Dolev, D.: Self-stabilization of byzantine protocols. In: 7th International Symposium on Self-Stabilizing Systems (SSS 2005), pp. 48–67 (2005)

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

    Article  Google Scholar 

  11. Delaët, S., Ducourthial, B., Tixeuil, S.: Self-stabilization with r-operators revisited. J. Aerosp. Comput. Inf. Commun. 3(10), 498–514 (2006)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. Dolev, S., Welch, J.L.: Self-stabilizing clock synchronization in the presence of byzantine faults. J. ACM 51(5), 780–799 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Dolev, S., Israeli, A., Moran, S.: Self-stabilization of dynamic systems assuming only read/write atomicity. In: 9th Annual ACM Symposium on Principles of Distributed Computing (PODC 1990), pp. 103–117 (1990)

  16. 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 

  17. Dubois, S., Masuzawa, T., Tixeuil, S.: The impact of topology on byzantine containment in stabilization. In: 24th International Symposium on Distributed Computing (DISC 2010) (2010a)

  18. Dubois, S., Masuzawa, T., Tixeuil, S.: On byzantine containment properties of the min+1 protocol. In: 12th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2010) (2010b)

  19. Dubois, S., Masuzawa, T., Tixeuil. S.: Maximum metric spanning tree made byzantine tolerant. In: 25th International Symposium on Distributed Computing (DISC 2011) (2011)

  20. Dubois, S., Masuzawa, T., Tixeuil, S.: Bounding the impact of unbounded attacks in stabilization. IEEE Trans. Parallel Distrib. Syst. 23(3), 460–466 (2012)

    Article  Google Scholar 

  21. Ducourthial, B., Tixeuil, S.: Self-stabilization with r-operators. Distrib. Comput. 14(3), 147–162 (2001)

    Article  Google Scholar 

  22. Ducourthial, B., Tixeuil, S.: Self-stabilization with path algebra. Theor. Comput. Sci. 293(1), 219–236 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. 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  MATH  Google Scholar 

  24. Gärtner, F.C.: A survey of self-stabilizing spanning-tree construction algorithms. Technical report ic/2003/38, EPFL (2003)

  25. Gouda, M.G., Schneider, M.: Maximum flow routing. In: Joint Conference on Information Sciences (JCIS 1994) (1994)

  26. Gouda, M.G., Schneider, M.: Stabilization of maximal metric trees. In: ICDCS Workshop on Self-stabilizing Systems (WSS 1999), pp. 10–17 (1999)

  27. Gouda, M.G., Schneider, M.: Maximizable routing metrics. IEEE/ACM Trans. Netw. 11(4), 663–675 (2003)

    Article  Google Scholar 

  28. Huang, S.T., Chen, N.S.: A self-stabilizing algorithm for constructing breadth-first trees. Inf. Process. Lett. 41(2), 109–117 (1992)

    Article  MATH  Google Scholar 

  29. Huang, S.T., Wuu, L.C.: Self-stabilizing token circulation in uniform networks. Distrib. Comput. 10(4), 181–187 (1997)

    Article  Google Scholar 

  30. Huang, T.C., Lin, J.C.: A self-stabilizing algorithm for the shortest path problem in a distributed system. Comput. Math. Appl. 43(1–2), 103–109 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  31. Lamport, L., Shostak, R.E., Pease, M.C.: The byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)

    Article  MATH  Google Scholar 

  32. Masuzawa, T., Tixeuil, S.: Stabilizing link-coloration of arbitrary networks with unbounded byzantine faults. Int. J. Princ. Appl. Inf. Sci. Technol. 1(1), 1–13 (2007)

    Google Scholar 

  33. Nesterenko, M., Arora, A.: Tolerance to unbounded byzantine faults. In: 21st Symposium on Reliable Distributed Systems (SRDS 2002), pp. 22–29. IEEE Computer Society (2002)

  34. Schneider, M.: Flow routing in computer networks. PhD thesis, University of Texas at Austin (1997)

  35. Tixeuil, S.: Self-stabilizing algorithms. Applied algorithms and data structures. Algorithms and Theory of Computation Handbook, 2nd edn, pp. 26.1–26.45. CRC Press, Taylor & Francis Group, Boca Raton (2009)

    Google Scholar 

  36. Tsai, M.S., Huang, S.T.: A self-stabilizing algorith for the shortest paths problem with a fully distributed demon. Parallel Process. Lett. 4, 65–72 (1994)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported in part by ANR projects SHAMAN, ALADDIN and SPADES and by Global COE (Centers of Excellence) Program of MEXT and Grant-in-Aid for Scientific Research (B)22300009 of JSPS

Author information

Authors and Affiliations

  1. Sorbonne Universités, UPMC Université Paris 6, Équipe REGAL, LIP6 CNRS, UMR 7606, LIP6 Inria, Équipe-projet REGAL, LIP6, Case 26-00/207, 5 place Jussieu, 75252, Paris Cedex 05, France

    Swan Dubois

  2. Osaka University, Yamadaoka 1-5, Suita, Osaka, 565-0871, Japan

    Toshimitsu Masuzawa

  3. Sorbonne Universités, UPMC Université Paris 6, Équipe REGAL, LIP6 CNRS, UMR 7606, LIP6 Institut Universitaire de France Case 26-00/113, 5 place Jussieu, 75252, Paris Cedex 05, France

    Sébastien Tixeuil

Authors
  1. Swan Dubois
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Toshimitsu Masuzawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sébastien Tixeuil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Swan Dubois.

Additional information

A preliminary version of this work appears in the proceedings of the 25th and of the 24th International Symposium on Distributed Computing (DISC’10 and DISC’11), see [17, 19].

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dubois, S., Masuzawa, T. & Tixeuil, S. Maximum Metric Spanning Tree Made Byzantine Tolerant. Algorithmica 73, 166–201 (2015). https://doi.org/10.1007/s00453-014-9913-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-014-9913-5

Keywords

Search

Navigation