A Randomized Algorithm for Online Unit Clustering

@article{Chan2006ARA,
  title={A Randomized Algorithm for Online Unit Clustering},
  author={Timothy M. Chan and Hamid Zarrabi-Zadeh},
  journal={Theory of Computing Systems},
  year={2006},
  volume={45},
  pages={486-496}
}
In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used. In the one-dimensional case, we show that surprisingly the naïve upper bound of 2 on the competitive ratio can be beaten: we present a new randomized 15/8-competitive online algorithm. We also provide some lower bounds and an extension to higher dimensions.