# A Tree Structure For Dynamic Facility Location

arXiv: https://arxiv.org/abs/1909.06653 · HTML: https://mlsanity.com/paper/1909.06653/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2019.

## Built on by (most cited first, 1 of 1)

- [Dynamic algorithms for k-center on graphs](https://mlsanity.com/paper/2307.15557/) (2023)

## Abstract (arXiv)

We study the metric facility location problem with client insertions and deletions. This setting differs from the classic dynamic facility location problem, where the set of clients remains the same, but the metric space can change over time. We show a deterministic algorithm that maintains a constant factor approximation to the optimal solution in worst-case time tilde O(2O(kappa2)) per client insertion or deletion in metric spaces while answering queries about the cost in O(1) time, where kappa denotes the doubling dimension of the metric. For metric spaces with bounded doubling dimension, the update time is polylogarithmic in the parameters of the problem.