Optimal gradient clock synchronization in dynamic networks

Fabian Kuhn, Christoph Lenzen, Thomas Locher, Rotem Oshman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study the problem of clock synchronization in highly dynamic networks, where communication links can appear or disappear at any time. The nodes in the network are equipped with hardware clocks, but the rate of the hardware clocks can vary arbitrarily within specific bounds, and the estimates that nodes can obtain about the clock values of other nodes are inherently inaccurate. Our goal in this setting is to output a logical clock at each node, such that the logical clocks of any two nodes are not too far apart, and nodes that remain close to each other in the network for a long time are better synchronized than distant nodes. This property is called gradient clock synchronization. Gradient clock synchronization has been widely studied in the static setting. We show that the bounds for the static case also apply to our highly dynamic setting: if two nodes remain at distance d from each other for sufficiently long, it is possible to synchronize their clocks to within O(d log(D/d)), where D is the diameter of the network. This is known to be optimal for static networks, and since a static network is a special case of a dynamic network, it is optimal for dynamic networks as well. Furthermore, we show that our algorithm has optimal stabilization time: when a path of length d appears between two nodes, the time required until the skew between the two nodes is reduced to O(d log(D/d)) is O(D), which we prove is optimal.

Original languageEnglish
Title of host publicationPODC'10 - Proceedings of the 2010 ACM Symposium on Principles of Distributed Computing
Number of pages10
StatePublished - 2010
Externally publishedYes
Event29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2010 - Zurich, Switzerland
Duration: 25 Jul 201028 Jul 2010

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2010


  • Clock synchronization
  • Dynamic networks


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