Skip to main content
Springer Nature Link
Log in

An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults

  • Conference paper
  • First Online:
Stabilization, Safety, and Security of Distributed Systems (SSS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10616))

Abstract

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model proposed by Garay ’94 – in the model, an omniscient adversary can corrupt up to f nodes in each round, and at the beginning of each round, faults may “move” in the system (i.e., different sets of nodes may become faulty in different rounds). Recent work by Bonomi et al. ’16 proposed a simple iterative approximate consensus algorithm which requires at least \(4f+1\) nodes. This paper proposes a novel technique of using “confession” (a mechanism to allow other nodes to ignore past behavior) and a variant of reliable broadcast to improve the fault-tolerance level. In particular, we present an approximate consensus algorithm that requires only \(\lceil 7f/2\rceil + 1\) nodes, an \(\lfloor f/2 \rfloor \) improvement over the state-of-the-art algorithms. Moreover, we also show that the proposed algorithm is optimal within a family of round-based algorithms.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Using the technique from [1], nodes can also estimate the number of required rounds and decide when to “output” the state variable v.

  2. 2.

    There are other scenarios not discussed in the proof for brevity; however, m is the only value that works for each of the scenarios.

References

  1. Abraham, I., Amit, Y., Dolev, D.: Optimal resilience asynchronous approximate agreement. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 229–239. Springer, Heidelberg (2005). doi:10.1007/11516798_17

    Chapter  Google Scholar 

  2. Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations, and Advanced Topics. Wiley Series on Parallel and Distributed Computing (2004)

    Google Scholar 

  3. Banu, N., Souissi, S., Izumi, T., Bessani, A.N., Correia, M., Neves, N.F., Buhrman, H., Garay, J.A.: An improved Byzantine agreement algorithm for synchronous systems with mobile faults (2012)

    Google Scholar 

  4. Bonnet, F., Défago, X., Nguyen, T.D., Potop-Butucaru, M.: Tight bound on mobile Byzantine agreement. In: Kuhn, F. (ed.) DISC 2014. LNCS, vol. 8784, pp. 76–90. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45174-8_6

    Chapter  Google Scholar 

  5. Bonomi, S., Pozzo, A.D., Potop-Butucaru, M., Tixeuil, S.: Approximate agreement under mobile Byzantine faults. CoRR, abs/1604.03871 (2016)

    Google Scholar 

  6. Bonomi, S., Pozzo, A.D., Potop-Butucaru, M., Tixeuil, S.: Approximate agreement under mobile Byzantine faults. In: 2016 IEEE 36th International Conference on Distributed Computing Systems (ICDCS), pp. 727–728, June 2016

    Google Scholar 

  7. Buhrman, H., Garay, J.A., Hoepman, J.H.: Optimal resiliency against mobile faults. In: Twenty-Fifth International Symposium on Fault-Tolerant Computing. Digest of Papers, pp. 83–88, June 1995

    Google Scholar 

  8. Dolev, D., Lynch, N.A., Pinter, S.S., Stark, E.W., Weihl, W.E.: Reaching approximate agreement in the presence of faults. J. ACM 33, 499–516 (1986)

    Article  MathSciNet  Google Scholar 

  9. Garay, J.A.: Reaching (and maintaining) agreement in the presence of mobile faults. In: Tel, G., Vitányi, P. (eds.) WDAG 1994. LNCS, vol. 857, pp. 253–264. Springer, Heidelberg (1994). doi:10.1007/BFb0020438

    Chapter  Google Scholar 

  10. Haseltalab, A., Akar, M.: Approximate Byzantine consensus in faulty asynchronous networks. In: 2015 American Control Conference (ACC), July 2015

    Google Scholar 

  11. Jadbabaie, A., Lin, J., Morse, A.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

  12. Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information, pp. 482–491. IEEE Computer Society (2003)

    Google Scholar 

  13. Kieckhafer, R.M., Azadmanesh, M.H.: Reaching approximate agreement with mixed-mode faults. IEEE Trans. Parallel Distrib. Syst. 5(1), 53–63 (1994)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann, Burlington (1996)

    MATH  Google Scholar 

  16. Ostrovsky, R., Yung, M.: How to withstand mobile virus attacks (extended abstract). In: Proceedings of the Tenth Annual ACM Symposium on Principles of Distributed Computing, PODC 1991. ACM (1991)

    Google Scholar 

  17. Sasaki, T., Yamauchi, Y., Kijima, S., Yamashita, M.: Mobile Byzantine agreement on arbitrary network. In: Baldoni, R., Nisse, N., van Steen, M. (eds.) OPODIS 2013. LNCS, vol. 8304, pp. 236–250. Springer, Cham (2013). doi:10.1007/978-3-319-03850-6_17

    Chapter  Google Scholar 

  18. Schizas, I., Ribeiro, A., Giannakis, G.: Consensus in ad hoc WSNs with noisy links - Part I: distributed estimation of deterministic signals. IEEE Trans. Sig. Process. 56(1), 350–364 (2008)

    Article  Google Scholar 

  19. Tseng, L., Vaidya, N.: Iterative approximate consensus in the presence of Byzantine link failures. In: Noubir, G., Raynal, M. (eds.) NETYS 2014. LNCS, vol. 8593, pp. 84–98. Springer, Cham (2014). doi:10.1007/978-3-319-09581-3_7

    Chapter  Google Scholar 

  20. Vaidya, N.H., Tseng, L., Liang, G.: Iterative approximate Byzantine consensus in arbitrary directed graphs. In: PODC 2012 (2012)

    Google Scholar 

  21. Yung, M.: The mobile adversary paradigm in distributed computation and systems. In: PODC 2015 (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science, Boston College, Boston, MA, USA

    Lewis Tseng

Authors
  1. Lewis Tseng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lewis Tseng .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Paul Spirakis

  2. Chalmers University of Technology, Gothenburg, Sweden

    Philippas Tsigas

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Tseng, L. (2017). An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-69084-1_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69083-4

  • Online ISBN: 978-3-319-69084-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics