New Algorithms for Fully-Dynamic k-center with Outliers

Abstract

In this paper, we study the fully dynamic k-center with outliers problem, where points are inserted and deleted over time and the goal is to maintain an approximate clustering while discarding up to z outliers. Existing algorithms typically rely on radius guessing to maintain cluster representations, leading to update and query times that depend explicitly on the aspect ratio Δ. We propose a layered-sampling framework that avoids radius guessing by maintaining a hierarchy of sampled structures, which can separate most inliers from potential outliers and refine the remaining uncertain points. The resulting algorithm achieves $\tilde{O}(k^2/\epsilon^4)$ update and query time independent of Δ, while guaranteeing a constant-factor approximation with $(1+\epsilon)z$ outliers discarded. Under mild assumptions, our result is complemented by a lower bound in metric space query model.