Journal of the ACM (JACM)
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
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
Brief announcement: gradient clock synchronization in sensor networks
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Tight bounds for clock synchronization
Proceedings of the 28th ACM symposium on Principles of distributed computing
Gradient clock synchronization in wireless sensor networks
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
Optimal clock synchronization in networks
Proceedings of the 7th ACM Conference on Embedded Networked Sensor Systems
Tight bounds for clock synchronization
Journal of the ACM (JACM)
Clock Synchronization: Open Problems in Theory and Practice
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Sensor networks continue to puzzle: selected open problems
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
Algorithms for sensor and ad hoc networks: advanced lectures
Algorithms for sensor and ad hoc networks: advanced lectures
Optimal gradient clock synchronization in dynamic networks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Oblivious gradient clock synchronization
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Clock synchronization for wireless networks
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
Optimal clock synchronization under energy constraints in wireless ad-hoc networks
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
D-Zipfian: a decentralized implementation of Zipfian
Proceedings of the Sixth International Workshop on Testing Database Systems
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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. 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 from each other is Ω(d + log Dlog 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.