Online Unit Covering in Euclidean Space

We revisit the online Unit Covering problem in higher dimensions: Given a set of n points in \(\mathbb {R}^d\), that arrive one by one, cover the points by balls of unit radius, so as to minimize the number of balls used. In this paper, we work in \(\mathbb {R}^d\) using Euclidean distance. The current best competitive ratio of an online algorithm, \(O(2^d d \log {d})\), is due to Charikar et al. (2004); their algorithm is deterministic.

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