Reallocating multiple facilities on the line

Fotakis, Dimitris; Kavouras, Loukas; Kostopanagiotis, Panagiotis; Lazos, Philip; Skoulakis, Stratis; Zarifis, Nikos

doi:10.1016/j.tcs.2021.01.028

Cited by 9 publications

(3 citation statements)

References 15 publications

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“…In the online version of the k-facility reallocation problem, we have more than one customer points that request service at each time step, instead of one request at a time as in the abstract online problem. Fotakis et al [13] present a constant-competitive algorithm for this setting when k = 2 on the lines.…”

Section: Related Workmentioning

confidence: 99%

Toward Online Mobile Facility Location on General Metrics

Ghodselahi,

Kuhn

2023

Theory Comput Syst

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We introduce an online variant of mobile facility location (MFL) (introduced by Demaine et al. (SODA 258–267 2007)). We call this new problem online mobile facility location (OMFL). In the OMFL problem, initially, we are given a set of k mobile facilities with their starting locations. One by one, requests are added. After each request arrives, one can make some changes to the facility locations before the subsequent request arrives. Each request is always assigned to the nearest facility. The cost of this assignment is the distance from the request to the facility. The objective is to minimize the total cost, which consists of the relocation cost of facilities and the distance cost of requests to their nearest facilities. We provide a lower bound for the OMFL problem that even holds on uniform metrics. A natural approach to solve the OMFL problem for general metric spaces is to utilize hierarchically well-separated trees (HSTs) and directly solve the OMFL problem on HSTs. In this paper, we provide the first step in this direction by solving a generalized variant of the OMFL problem on uniform metrics that we call G-OMFL. We devise a simple deterministic online algorithm and provide a tight analysis for the algorithm. The second step remains an open question. Inspired by the k-server problem, we introduce a new variant of the OMFL problem that focuses solely on minimizing movement cost. We refer to this variant as M-OMFL. Additionally, we provide a lower bound for M-OMFL that is applicable even on uniform metrics.

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Section: Related Workmentioning

confidence: 99%

Toward Online Mobile Facility Location on General Metrics

Ghodselahi,

Kuhn

2023

Theory Comput Syst

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“…Their goal is to minimize the total travel distance of agents and the facility. Later, Fotakis et al (2021) generalized the problem to relocate k facilities where the optimal solution can be computed in polynomial time. In their settings, the facility serves all agents at each stage, and the served agents stay in the system with different locations in each stage.…”

Section: Related Workmentioning

confidence: 99%

Multi-Stage Facility Location Problems with Transient Agents

Wang

Chau²,

Chan

et al. 2023

AAAI

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We study various models for the one-dimensional multi-stage facility location problems with transient agents, where a transient agent arrives in some stage and stays for a number of consecutive stages. In the problems, we need to serve each agent in one of their stages by determining the location of the facility at each stage. In the first model, we assume there is no cost for moving the facility across the stages. We focus on optimal algorithms to minimize both the social cost objective, defined as the total distance of all agents to the facility over all stages, and the maximum cost objective, defined as the max distance of any agent to the facility over all stages. For each objective, we give a slice-wise polynomial (XP) algorithm (i.e., solvable in m^f(k) for some fixed parameter k and computable function f, where m is the input size) and show that there is a polynomial-time algorithm when a natural first-come-first-serve (FCFS) order of agent serving is enforced. We then consider the mechanism design problem, where the agents' locations and arrival stages are private, and design a group strategy-proof mechanism that achieves good approximation ratios for both objectives and settings with and without FCFS ordering. In the second model, we consider the facility's moving cost between adjacent stages under the social cost objective, which accounts for the total moving distance of the facility. Correspondingly, we design XP (and polynomial time) algorithms and a group strategy-proof mechanism for settings with or without the FCFS ordering.

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“…Most of the work on the problem assumes a static model, in which the agents' locations are fixed over time. Exceptions to this are two fairly recent works [De Keijzer and Wojtczak, 2018;Fotakis et al, 2021] who considered multi-stage facility reallocation problems on the real line, where the facilities are being moved between stages based on the locations reported by the agents and the goal is to minimize the social cost by keeping the reallocation cost low as well. Another exception is the work of Wada et al [2018], who investigated settings with variable and dynamic populations, affecting the choices of the designer.…”

Section: Future Research Directionsmentioning

confidence: 99%

Mechanism Design for Facility Location Problems: A Survey

Chan

Filos-Ratsikas

et al. 2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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The study of approximate mechanism design for facility location has been in the center of research at the intersection of artificial intelligence and economics for the last decade, largely due to its practical importance in various domains, such as social planning and clustering. At a high level, the goal is to select a number of locations on which to build a set of facilities, aiming to optimize some social objective based on the preferences of strategic agents, who might have incentives to misreport their private information. This paper presents a comprehensive survey of the significant progress that has been made since the introduction of the problem, highlighting all the different variants and methodologies, as well as the most interesting directions for future research.

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Reallocating multiple facilities on the line

Cited by 9 publications

References 15 publications

Toward Online Mobile Facility Location on General Metrics

Toward Online Mobile Facility Location on General Metrics

Multi-Stage Facility Location Problems with Transient Agents

Mechanism Design for Facility Location Problems: A Survey

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