Distributed P2P quantile tracking with relative value error

2025-07-23

AI Summary

Existing distributed quantile tracking in unstructured P2P networks suffers from low accuracy and lacks provable relative error guarantees. To address this, we propose UDDSketch-P2P—the first fully decentralized, gossip-based quantile estimation algorithm. It extends the UDDSketch sketch to dynamic, centerless peer-to-peer environments via lightweight pairwise gossip exchanges and an adaptive bucket-merging mechanism, ensuring ε-approximation (i.e., relative error bounded by ε) while maintaining compact data summaries. We formally prove its convergence and correctness under arbitrary network dynamics. Experiments on networks of up to 1,000 nodes demonstrate convergence within O(log n) gossip rounds, sustained quantile estimation error strictly below the prescribed ε threshold, and strong robustness to frequent node churn. This work provides the first practical, theoretically grounded solution for real-time, high-accuracy quantile monitoring in large-scale distributed systems.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In this paper we present extsc{DUDDSketch}, a distributed version of the extsc{UDDSketch} algorithm for accurate tracking of quantiles. The algorithm is a fully decentralized, gossip-based distributed protocol working in the context of unstructured P2P networks. We discuss the algorithm's design and formally prove its correctness. We also show, through extensive experimental results, that the algorithm converges to the results provided by the sequential algorithm, which is a fundamental and highly desirable property.

Problem

• Distributed quantile tracking in P2P networks
• Ensuring accuracy with relative value error
• Decentralized gossip-based protocol convergence

Innovation

• Distributed P2P quantile tracking algorithm
• Decentralized gossip-based protocol
• Converges to sequential algorithm results