Synchronizing clocks in the presence of faults
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A new fault-tolerant algorithm for clock synchronization
Information and Computation
A theory of clock synchronization (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Optimal and efficient clock synchronization under drifting clocks
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
Closed form bounds for clock synchronization under simple uncertainty assumptions
Information Processing Letters
Broadcast scheduling for TDMA in wireless multihop networks
Handbook of wireless networks and mobile computing
Fine-grained network time synchronization using reference broadcasts
ACM SIGOPS Operating Systems Review - OSDI '02: Proceedings of the 5th symposium on Operating systems design and implementation
Timed I/O Automata: A Mathematical Framework for Modeling and Analyzing Real-Time Systems
RTSS '03 Proceedings of the 24th IEEE International Real-Time Systems Symposium
An algorithm for clock synchronization with the gradient property in sensor networks
Journal of Parallel and Distributed Computing
Gradient clock synchronization in dynamic networks
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Analysis of a Clock Synchronization Protocol for Wireless Sensor Networks
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Gradient Clock Synchronization Using Reference Broadcasts
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Analysis of a clock synchronization protocol for wireless sensor networks
Theoretical Computer Science
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We introduce the distributed gradient clock synchronization problem. As in traditional distributed clock synchronization, we consider a network of nodes equipped with hardware clocks with bounded drift. Nodes compute logical clock values based on their hardware clocks and message exchanges, and the goal is to synchronize the nodes' logical clocks as closely as possible, while satisfying certain validity conditions. The new feature of gradient clock synchronization (GCS for short) is to require that the skew between any two nodes' logical clocks be bounded by a nondecreasing function of the uncertainty in message delay (call this the distance) between the two nodes, and other network parameters. That is, we require nearby nodes to be closely synchronized, and allow faraway nodes to be more loosely synchronized. We contrast GCS with traditional clock synchronization, and discuss several practical motivations for GCS, mostly arising in sensor and ad-hoc networks. Our main result is that the worst case clock skew between two nodes at distance d or less from each other is Ω (d+log D/log log D), where D is the diameter1 of the network. This means that clock synchronization is not a local property, in the sense that the clock skew between two nodes depends not only on the distance between the nodes, but also on the size of the network. Our lower bound implies, for example, that the TDMA protocol with a fixed slot granularity will fail as the network grows, even if the maximum degree of each node stays constant.