Oblivious gradient clock synchronization

We study the gradient clock synchronization (GCS) problem, in which the worst-case clock skew between neighboring nodes has to be minimized. In particular, we consider oblivious clock synchronization algorithms which base their decision on how to adapt the clock solely on the most accurate timing information received from each neighbor. For several intuitive clock synchronization algorithms, which attempt to minimize the skew at all times, we show that the clock skew between neighboring nodes can be significantly larger than the proven lower bound of $\Omega(\frac{\log D}{\log\log D})$, where D denotes the diameter of the network. All of these natural algorithms belong to the class of oblivious clock synchronization algorithms. Additionally, we present an oblivious algorithm with a worst-case skew of $O(d + \sqrt{D})$ between any two nodes at distance d.