Online facility location with facility movements

Divéki, Gabriella; Imreh, Csanád

doi:10.1007/s10100-010-0153-8

Cited by 28 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is di erent to the situation for o ine algorithms where the complete input data is known before the computations are made. Online algorithms appear in many di erent scenarios/environments -mobile computing [7], operating systems and resource allocation [13], facility location problems [10,4,6], theoretical computer science [2,5], etc. Typically no changes are made to the decisions made at each iteration of an online algorithm although some online algorithms do allow some limited amending of the decisions made previously when new data is encountered [4].…”

Section: Online Algorithmsmentioning

confidence: 99%

Cooperating to buy shoes in the real world

Sanders

2013

Proceedings of the South African Institute for Computer Scientists and Information Technologists Conference

View full text Add to dashboard Cite

There are many people who have di erent size feet and need di erent sizes of shoes to get shoes that fit well. A static approach to solving the problem could be to get a list of all the people who need shoes and their size requirements, then from that list find groups of people who can cooperate. In a graph theory sense this means creating a directed graph from the input data, finding all of the simple cycles in the graph and then picking the smallest set of cycles such that each node in a cycle in the original graph is in at least one cycle in the final set of cycles.This paper looks at a more dynamic approach of dealing with the problem. People who need shoes enter the system, by giving their shoe size requirements, and remain in the system until their needs have been satisfied. This approach is represented by an online algorithm which stores all the possible paths in the graph at any stage, checks for cycles when a new person enters the system and updates appropriately in each iteration. The online algorithm can also accommodate "altruism" (where an individual chooses to stay in the system to assist others to buy shoes) and spreading the cost of buying additional pairs of shoes (for example, two people buying three pairs of shoes) in order for individuals to more quickly have their shoe needs satisfied. The three versions of the online algorithm were implemented and tested on synthetic data. The online algorithm generally satisfies the needs of the people entering the system although its performance is sometimes a ected by the lack of knowledge of the entire input set.

show abstract

Section: Online Algorithmsmentioning

confidence: 99%

Cooperating to buy shoes in the real world

Sanders

2013

Proceedings of the South African Institute for Computer Scientists and Information Technologists Conference

View full text Add to dashboard Cite

show abstract

“…In this time dependent variant of facility location, agents may change their location over time and we look for the best tradeoff between the optimal connections of agents to facilities and the stability of solutions between [15] for a survey. DivÃľki and Imreh [11] studied an online model, where facilities can be moved with zero cost. As we have mentioned before, the online variant of the K-facility reallocation problem is a generalization of the K-server problem, which is one of the most natural online problems.…”

Section: Introductionmentioning

confidence: 99%

Reallocating Multiple Facilities on the Line

Fotakis

Kavouras

Kostopanagiotis

et al. 2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

View full text Add to dashboard Cite

We study the multistage K-facility reallocation problem on the real line, where we maintain K facility locations over T stages, based on the stage-dependent locations of n agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. K-facility reallocation was introduced by de Keijzer and Wojtczak [10], where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider online K-facility reallocation, where the algorithm becomes aware of agent locations in a stage-by-stage fashion. By exploiting an interesting connection to the classical K-server problem, we present a constant-competitive algorithm for K = 2 facilities. 1 consecutive timesteps. The stability of the solutions is modeled by introducing an additional moving cost (or switching cost), which has a different definition depending on the particular setting. Model and Motivation.In this work, we study the multistage K-facility reallocation problem on the real line, introduced by de Keijzer and Wojtczak [10]. In K-facility reallocation, K facilities are initially located at (x 0 1 , . . . , x 0 K ) on the real line. Facilities are meant to serve n agents for the next T days. At each day, each agent connects to the facility closest to its location and incurs a connection cost equal to this distance. The locations of the agents may change every day, thus we have to move facilities accordingly in order to reduce the connection cost. Naturally, moving a facility is not for free, but comes with the price of the distance that the facility was moved. Our goal is to specify the exact positions of the facilities at each day so that the total connection cost plus the total moving cost is minimized over all T days. In the online version of the problem, the positions of the agents at each stage t are revealed only after determining the locations of the facilities at stage t − 1.For a motivating example, consider a company willing to advertise its products. To this end, it organizes K advertising campaigns at different locations of a large city for the next T days. Based on planned events, weather forecasts, etc., the company estimates a population distribution over the locations of the city for each day. Then, the company decides to compute the best possible campaign reallocation with K campaigns over all days (see also [10] for more examples).de Keijzer and Wojtczak [10] fully characterized the optimal offline and online algorithms for the special case of a single facility and presented a dynamic programming algorithm for K ≥ 1 facilities with running time exponential in K. Despite the practical significance and the interesting theoretical properties of Kfacility reallocation, its computationa...

show abstract

“…Later, Fotakis [11] showed an asymptotically tight competitive ratio of Θ(log n/log log n). Online problems have also been studied under varying assumptions to give constant competitive algorithms: Anagnostopoulos, Bent, Upfal, and Hentenryck [1] studied the case where the clients are drawn from a known distribution; Fotakis [10] presented an algorithm for the case where the reassignment of clients is allowed; Divéki and Imreh [8] considered a setting that allows us to move facilities.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Facility Location via Exponential Clocks

AnHyung-Chan¹,

Norouzi-FardAshkan²,

SvenssonOla³

2017

ACM Trans. Algorithms

View full text Add to dashboard Cite

The dynamic facility location problem is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the "stability" of the solution: there is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches.We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities, and connect every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP-roundings for facility location problems. In particular, we use no clustering and we allow clients to connect through paths of arbitrary lengths. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem.

show abstract

Online facility location with facility movements

Cited by 28 publications

References 12 publications

Cooperating to buy shoes in the real world

Cooperating to buy shoes in the real world

Reallocating Multiple Facilities on the Line

Dynamic Facility Location via Exponential Clocks

Contact Info

Product

Resources

About