Theory of Computing Systems

, Volume 49, Issue 4, pp 781–816 | Cite as

Gradient Clock Synchronization in Dynamic Networks

  • Fabian Kuhn
  • Thomas Locher
  • Rotem Oshman


Over the last years, large-scale decentralized computer networks such as peer-to-peer and mobile ad hoc networks have become increasingly prevalent. The topologies of many of these networks are often highly dynamic. This is especially true for ad hoc networks formed by mobile wireless devices.

In this paper, we study the fundamental problem of clock synchronization in dynamic networks. We show that there is an inherent trade-off between the skew \(\mathcal{S}\) guaranteed along sufficiently old links and the time needed to guarantee a small skew along new links: for any sufficiently large initial skew on a new link, there are executions in which the time required to reduce the skew on the link to \(O(\mathcal{S})\) is at least \(\Omega(n/\mathcal{S})\).

We show that this bound is tight for moderately small values of \(\mathcal{S}\). Assuming a fixed set of n nodes, an arbitrary pattern of edge insertions and removals, and a weak dynamic connectivity requirement, we present an algorithm that always maintains a skew of O(n) between any two nodes in the network. For a parameter \(\mathcal{S}=\Omega(\sqrt{\rho n})\), where ρ is the maximum hardware clock drift, it is further guaranteed that if a communication link between two nodes u,v persists in the network for \(\Theta(n/\mathcal{S})\) time, the clock skew between u and v is reduced to no more than \(O(\mathcal{S})\).


Distributed algorithms Dynamic networks Gradient clock synchronization Lower bound 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Attiya, H., Herzberg, A., Rajsbaum, S.: Optimal clock synchronization under different delay assumptions. SIAM J. Comput. 25(2), 369–389 (1996) MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Attiya, H., Hay, D., Welch, J.L.: Optimal clock synchronization under energy constraints in wireless ad-hoc networks. In: Proc. of 9th Int. Conf. on Principles of Distributed Systems (OPODIS), pp. 221–234 (2005) Google Scholar
  3. 3.
    Biaz, S., Welch, J.L.: Closed form bounds for clock synchronization under simple uncertainty assumptions. Inf. Process. Lett. 80(3), 151–157 (2001) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Dolev, D., Halpern, J.Y., Strong, H.R.: On the possibility and impossibility of achieving clock synchronization. J. Comput. Syst. Sci. 32(2), 230–250 (1986) MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Dolev, D., Halpern, J.Y., Simons, B., Strong, R.: Dynamic fault-tolerant clock synchronization. J. ACM 42(1), 143–185 (1995) zbMATHGoogle Scholar
  6. 6.
    Elson, J., Girod, L., Estrin, D.: Fine-grained network time synchronization using reference broadcasts. Oper. Syst. Rev. 36(SI), 147–163 (2002) CrossRefGoogle Scholar
  7. 7.
    Fan, R., Lynch, N.: Gradient clock synchronization. Distrib. Comput. 18(4), 255–266 (2006) CrossRefGoogle Scholar
  8. 8.
    Fan, R., Chakraborty, I., Lynch, N.: Clock synchronization for wireless networks. In: Proc. of 8th Int. Conf. on Principles of Distributed Systems (OPODIS), pp. 400–414 (2004) Google Scholar
  9. 9.
    Kaynar, D., Lynch, N., Segala, R., Vaandrager, F.: The Theory of Timed I/O Automata. Synthesis Lectures in Computer Science. Morgan & Claypool Publishers, San Rafael (2006) Google Scholar
  10. 10.
    Kuhn, F., Lenzen, C., Locher, T., Oshman, R.: Optimal gradient clock synchronization in dynamic networks. In: Richa, A.W., Guerraoui, R. (eds.) PODC, pp. 430–439. ACM, New York (2010) Google Scholar
  11. 11.
    Lamport, L., Melliar-Smith, P.M.: Synchronizing clocks in the presence of faults. J. ACM 32(1), 52–78 (1985) MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Lenzen, C., Locher, T., Wattenhofer, R.: Clock synchronization with bounded global and local skew. In: Prof. of 49th IEEE Symp. on Foundations of Computer Science (FOCS), pp. 500–510 (2008) Google Scholar
  13. 13.
    Lenzen, C., Locher, T., Wattenhofer, R.: Tight bounds for clock synchronization. In: Proc. of 28th ACM Symp. on Principles of Distributed Computing (PODC) (2009) Google Scholar
  14. 14.
    Locher, T., Wattenhofer, R.: Oblivious gradient clock synchronization. In: Proc. of 20th Int. Symp. on Distributed Computing (DISC), pp. 520–533 (2006) Google Scholar
  15. 15.
    Lundelius, J., Lynch, N.: An upper and lower bound for clock synchronization. Inf. Control 62(2/3), 190–204 (1984) MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996) zbMATHGoogle Scholar
  17. 17.
    Marzullo, K., Owicki, S.: Maintaining the time in a distributed system. In: Proc. of 2nd ACM Symp. on Principles of Distributed Computing (PODC), pp. 44–54 (1983) Google Scholar
  18. 18.
    Ostrovsky, R., Patt-Shamir, B.: Optimal and efficient clock synchronization under drifting clocks. In: Proc. of 18th ACM Symp. on Principles of Distributed Computing (PODC), pp. 400–414 (1999) Google Scholar
  19. 19.
    Patt-Shamir, B., Rajsbaum, S.: A theory of clock synchronization. In: Proc. of 26th ACM Symp. on Theory of Computing (STOC), pp. 810–819 (1994) Google Scholar
  20. 20.
    Srikanth, T.K., Toueg, S.: Optimal clock synchronization. J. ACM 34(3), 626–645 (1987) MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of InformaticsUniversity of LuganoLuganoSwitzerland
  2. 2.Computer Engineering and Networks LaboratoryETH ZurichZurichSwitzerland
  3. 3.Computer Science and Artificial Intelligence LaboratoryMITCambridgeUSA

Personalised recommendations