Gradient Clock Synchronization with Practically Constant Local Skew

TL;DR

This paper introduces a refined model and analysis for Gradient Clock Synchronization, achieving near-optimal local skew bounds under realistic stability assumptions, surpassing previous theoretical limits.

Contribution

It provides a novel analysis that relaxes worst-case assumptions, enabling practical synchronization with improved bounds and self-stabilization in dynamic network conditions.

Findings

Bounded local skew by O(Δ + δ log D) under realistic error stability assumptions.

Circumvents the Ω(Δ log D) lower bound when errors change slowly.

Achieves self-stabilization and extends results to external synchronization scenarios.

Abstract

Gradient Clock Synchronization (GCS) is the task of minimizing the \emph{local skew,} i.e., the clock offset between neighboring clocks, in a larger network. While asymptotically optimal bounds are known, from a practical perspective they have crucial shortcomings: - Local skew bounds are determined by upper bounds on offset estimation that need to be guaranteed throughout the entire lifetime of the system. - Worst-case frequency deviations of local oscillators from their nominal rate are assumed, yet frequencies tend to be much more stable in the (relevant) short term. State-of-the-art deployed synchronization methods adapt to the true offset measurement and frequency errors, but achieve no non-trivial guarantees on the local skew. In this work, we provide a refined model and novel analysis of existing techniques for solving GCS in this model. By requiring only \emph{stability} of measurement and frequency errors, we can circumvent existing lower bounds, leading to dramatic improvements under very general conditions. For example, if links exhibit a uniform worst-case estimation error of $\Delta$ and a \emph{change} in estimation errors of $\delta\ll \Delta$ on relevant time scales, we bound the local skew by $O(\Delta+\delta \log D)$ for networks of diameter $D$, effectively ``breaking'' the established $\Omega(\Delta\log D)$ lower bound, which holds when $\delta=\Delta$. Similarly, we show how to limit the influence of local oscillators on $\delta$ to scale with the \emph{change} of frequency of an individual oscillator on relevant time scales. Moreover, we show how to ensure self-stabilization in this challenging setting. Last, but not least, we extend all of our results to the scenario of external synchronization, at the cost of a limited increase in stabilization time.