A Tree Structure For Dynamic Facility Location

TL;DR

This paper introduces a deterministic algorithm for the dynamic facility location problem in metric spaces with client insertions and deletions, achieving constant approximation factors and efficient update times based on the doubling dimension.

Contribution

It presents the first deterministic algorithm with constant factor approximation and efficient update times for dynamic facility location in metric spaces with changing client sets.

Findings

Maintains constant factor approximation in worst-case time $ ilde O(2^{O( abla^2)})$ per update.

Achieves $O(1)$ query time for cost estimation.

Polylogarithmic update time for metric spaces with bounded doubling dimension.

Abstract

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 $\tilde O(2^{O(\kappa^2)})$ 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.