Communication-efficient Clock Synchronization

The problem of clock synchronization is studied in an arbitrary network ${\mathcal{G}} = ({\mathcal{V}},{\mathcal{E}})$ with $|{\mathcal{V}}|$ server nodes and $|{\mathcal{E}}|$ edges. Every pair of adjacent servers has a time discrepancy (edge information) that is only known approximately to one or both of the two adjacent servers. A master node aims to coordinate the otherwise independent clocks of the servers by eliminating the loop-wise offset surplus in the network. The goal is to minimize the communication cost between server nodes and the master node. Optimal schemes are found for the two cases where each time discrepancy is known by 1) both adjacent servers, and 2) only one of the adjacent servers. Notably, the scheme for the first case is robust to a straggler (slow or failed server). An algorithm that outperforms the natural (uncoded) baseline is proposed for the general setting that is a mix of the two cases. Classes of such mixed setting are identified where the algorithm represents the optimal solution.