A Simple and Robust Protocol for Distributed Counting

2025-09-06

AI Summary

This paper studies approximate counting over distributed adaptive event streams—where the stream’s behavior may dynamically change in response to the protocol’s outputs—under low communication cost. We first demonstrate that classical randomized counting protocols fail to guarantee robustness in such adaptive settings. To address this, we propose a novel, structurally simple protocol based on randomized sampling and rigorous error control. Our protocol achieves the optimal communication complexity of $O(sqrt{k}/varepsilon cdot log N)$, improving upon all existing robust solutions. Its correctness and accuracy are formally established via an adversarial analysis framework that accounts for adaptive stream modifications. The key contribution is bridging the theoretical gap between adaptivity-robustness and communication efficiency, proving that simplicity and robustness are simultaneously attainable in distributed approximate counting.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Adversarial Agents

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across $k$ sites while minimizing communication. The communication complexity of this problem is known to be $Θ(frac{k}εlog N)$ for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to $Θ(frac{sqrt{k}}εlog N)$, but their analysis is restricted to the {em oblivious setting}, where the stream of events is independent of the protocol's outputs. Xiong, Zhu, and Huang (2023) presented a robust protocol for distributed counting that removes the oblivious assumption. However, their communication complexity is suboptimal by a $polylog(k)$ factor and their protocol is substantially more complex than the oblivious protocol of Huang et al. (2012). This left open a natural question: could it be that the simple protocol of Huang et al. (2012) is already robust? We resolve this question with two main contributions. First, we show that the protocol of Huang et al. (2012) is itself not robust by constructing an explicit adaptive attack that forces it to lose its accuracy. Second, we present a new, surprisingly simple, robust protocol for distributed counting that achieves the optimal communication complexity of $O(frac{sqrt{k}}ε log N)$. Our protocol is simpler than that of Xiong et al. (2023), perhaps even simpler than that of Huang et al. (2012), and is the first to match the optimal oblivious complexity in the adaptive setting.

Problem

• Developing a robust distributed counting protocol
• Achieving optimal communication complexity adaptively
• Simplifying protocol design while maintaining accuracy

Innovation

• Robust distributed counting protocol
• Optimal communication complexity achieved
• Simpler than previous adaptive solutions