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Online Facility Location in Evolving Metrics

by 1,†, 1,*,† and 2,†
School of Electrical and Computer Engineering, National Technical University of Athens, 15780 Athens, Greece
Khoury College of Computer Science, Northeastern University, Boston, MA 02115, USA
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Frank Werner
Algorithms 2021, 14(3), 73;
Received: 18 January 2021 / Revised: 19 February 2021 / Accepted: 22 February 2021 / Published: 25 February 2021
(This article belongs to the Special Issue 2021 Selected Papers from Algorithms Editorial Board Members)
The Dynamic Facility Location problem is a generalization of the classic Facility Location problem, in which the distance metric between clients and facilities changes over time. Such metrics that develop as a function of time are usually called “evolving metrics”, thus Dynamic Facility Location can be alternatively interpreted as a Facility Location problem in evolving metrics. The objective in this time-dependent variant is to balance the trade-off between optimizing the classic objective function and the stability of the solution, which is modeled by charging a switching cost when a client’s assignment changes from one facility to another. In this paper, we study the online variant of Dynamic Facility Location. We present a randomized O(logm+logn)-competitive algorithm, where m is the number of facilities and n is the number of clients. In the first step, our algorithm produces a fractional solution, in each timestep, to the objective of Dynamic Facility Location involving a regularization function. This step is an adaptation of the generic algorithm proposed by Buchbinder et al. in their work “Competitive Analysis via Regularization.” Then, our algorithm rounds the fractional solution of this timestep to an integral one with the use of exponential clocks. We complement our result by proving a lower bound of Ω(m) for deterministic algorithms and lower bound of Ω(logm) for randomized algorithms. To the best of our knowledge, these are the first results for the online variant of the Dynamic Facility Location problem. View Full-Text
Keywords: dynamic facility location; online convex optimization; competitive analysis dynamic facility location; online convex optimization; competitive analysis
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MDPI and ACS Style

Fotakis, D.; Kavouras, L.; Zakynthinou, L. Online Facility Location in Evolving Metrics. Algorithms 2021, 14, 73.

AMA Style

Fotakis D, Kavouras L, Zakynthinou L. Online Facility Location in Evolving Metrics. Algorithms. 2021; 14(3):73.

Chicago/Turabian Style

Fotakis, Dimitris, Loukas Kavouras, and Lydia Zakynthinou. 2021. "Online Facility Location in Evolving Metrics" Algorithms 14, no. 3: 73.

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