Gradient Clock Synchronization with Practically Constant Local Skew

2025-11-03

AI Summary

Gradient Clock Synchronization (GCS) aims to minimize local clock offsets between neighboring nodes in large-scale networks. Existing asymptotically optimal protocols rely on a global worst-case frequency deviation assumption, yielding conservative bounds—specifically Ω(Δ log D)—and failing to adapt to short-term frequency stability or empirically observed measurement errors. This work proposes a novel GCS protocol: (1) a refined error model integrating dynamic measurement error tracking and local frequency stability analysis; (2) a breakthrough of the conventional lower bound, achieving an improved local offset upper bound of O(Δ + δ log D) when δ ≪ Δ; (3) single-oscillator frequency adaptation and self-stabilizing recovery; and (4) extension to external synchronization with bounded convergence overhead. Experiments demonstrate near-constant, tight local offset bounds across generic network topologies, significantly enhancing synchronization accuracy and robustness.

Technology Category

• Search and Optimization: Local Search
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Gradient Clock Synchronization (GCS) is the task of minimizing the 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 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 $Δ$ and a change in estimation errors of $δll Δ$ on relevant time scales, we bound the local skew by $O(Δ+δlog D)$ for networks of diameter $D$, effectively ``breaking'' the established $Ω(Δlog D)$ lower bound, which holds when $δ=Δ$. Similarly, we show how to limit the influence of local oscillators on $δ$ to scale with the change of frequency of an individual oscillator on relevant time scales, rather than a worst-case bound over all oscillators and the lifetime of the system. 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.

Problem

• Minimizing local clock skew between neighboring network nodes
• Overcoming impractical worst-case assumptions in synchronization models
• Achieving self-stabilization with improved bounds under realistic conditions

Innovation

• Refined model requiring only stability of measurement errors
• Novel analysis circumventing existing lower bounds on local skew
• Self-stabilization techniques extended to external synchronization scenarios