Dynamic k-center clustering with lifetimes

2026-03-24

AI Summary

This work studies the dynamic k-center clustering problem for data points with known lifetimes, bridging the gap between sliding-window and fully dynamic models. The authors introduce a novel dynamic clustering framework that accommodates arbitrary insertions and predictable deletions based on predefined lifespans. Within this model, they design a deterministic approximation algorithm that achieves a (2+ε)-approximation ratio with Õ(k/ε) amortized update time. Furthermore, under a mild assumption on the update sequence, the algorithm attains a (6+ε)-approximation ratio with Õ(k/ε) worst-case update time and heavily sublinear memory usage.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Data Stream Mining
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

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

Abstract

The $k$-center problem is a fundamental clustering variant with applications in learning systems and data summarization. In several real-world scenarios, the dataset to be clustered is not static, but evolves over time, as new data points arrive and old ones become stale. To account for dynamicity, the $k$-center problem has been mainly studied under the sliding window setting, where only the $N$ most recent points are considered non-stale, or the fully dynamic setting, where arbitrary sequences of point arrivals and deletions without prior notice may occur. In this paper, we introduce the dynamic setting with lifetimes, which bridges the two aforementioned classical settings by still allowing arbitrary arrivals and deletions, but making the deletion time of each point known upon its arrival. Under this new setting, we devise a deterministic $(2+\varepsilon)$-approximation algorithm with $\tilde{O}(k/\varepsilon)$ amortized update time and memory usage linear in the number of currently active points. Moreover, we develop a deterministic $(6+\varepsilon)$-approximation algorithm that, under tame update sequences, has $\tilde{O}(k/\varepsilon)$ worst-case update time and heavily sublinear working memory.

Problem

• dynamic k-center
• lifetimes
• clustering
• data summarization
• sliding window

Innovation

• dynamic k-center
• lifetimes
• approximation algorithm
• sublinear memory
• amortized update time