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New Results and Bounds on Online Facility Assignment Problem [article]

Saad Al Muttakee, Abu Reyan Ahmed, Md. Saidur Rahman
2020 arXiv   pre-print
Consider an online facility assignment problem where a set of facilities F = { f_1, f_2, f_3, ⋯, f_|F|} of equal capacity l is situated on a metric space and customers arrive one by one in an online manner  ...  Our bound is tight and better than the previous result. We also consider the facilities are distributed arbitrarily on a plane and provide an algorithm for the scenario.  ...  New results on  ... 
arXiv:2009.01446v1 fatcat:dd3qrkcpffawtfzi2scrhnrtbq

Online Facility Location with Deletions [article]

Marek Cygan and Artur Czumaj and Marcin Mucha and Piotr Sankowski
2018 arXiv   pre-print
When a client arrives, then it has to be assigned either to an existing facility or to a new facility opened at the client's location.  ...  In this paper we study three previously unstudied variants of the online Facility Location problem, considering an intrinsic scenario when the clients and facilities are not only allowed to arrive to the  ...  New results The main contribution of this paper is the first thorough study of the online Facility Location problem with deletions and design of new algorithms for this model in several natural settings  ... 
arXiv:1807.03839v1 fatcat:wuegicgnd5fivncvpwg3kfl75u

Online Facility Location with Deletions

Marek Cygan, Artur Czumaj, Marcin Mucha, Piotr Sankowski, Michael Wagner
2018 European Symposium on Algorithms  
When a client arrives, then it has to be assigned either to an existing facility or to a new facility opened at the client's location.  ...  In this paper we study three previously unstudied variants of the online Facility Location problem, considering an intrinsic scenario when the clients and facilities are not only allowed to arrive to the  ...  New results The main contribution of this paper is the first thorough study of the online Facility Location problem with deletions and design of new algorithms for this model in several natural settings  ... 
doi:10.4230/lipics.esa.2018.21 dblp:conf/esa/CyganCMS18 fatcat:a4xrwzrmsrcm3pjufual6mh75a

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship [article]

Ioannis Caragiannis, Aris Filos-Ratsikas, Soren Kristoffer Stiil Frederiksen, Kristoffer Arnsfelt Hansen, Zihan Tan
2016 arXiv   pre-print
We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space are assigned to facilities that lie on the metric space, under capacity constraints  ...  on the facilities.  ...  As we mentioned earlier, our results imply some bounds on the competitive ratio of the greedy algorithm for the online transportation problem.  ... 
arXiv:1602.08023v1 fatcat:pruwdfoqdrahrk6adwsv4xib7a

Online Mixed Packing and Covering [chapter]

Yossi Azar, Umang Bhaskar, Lisa Fleischer, Debmalya Panigrahi
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
We use ideas generated from our result for mixed packing and covering to obtain polylogarithmic-competitive algorithms for these problems.  ...  The success of this new framework for online optimization can be gauged from the fact that it has led to progress in several longstanding open questions.  ...  Clients arrive online, and each client j in C has an assignment cost a ij and a demand p ij on being assigned to facility i.  ... 
doi:10.1137/1.9781611973105.6 dblp:conf/soda/AzarBFP13 fatcat:jfo34xmwqnapnlx5n5jzqp5xvi

Online Facility Location with Multiple Advice

Matteo Almanza, Flavio Chierichetti, Silvio Lattanzi, Alessandro Panconesi, Giuseppe Re
2021 Neural Information Processing Systems  
In this paper, we study the classic facility location problem in the presence of multiple machine-learned advice.  ...  We design an algorithm with provable performance guarantees such that, if the advice is good, it outperforms the best-known online algorithms for the problem, and if it is bad it still matches their performance  ...  Acknowledgements This work was supported in part by a Google Focused Research Award, by the PRIN project 2017K7XPAN, by BiCi -Bertinoro international Center for informatics, and by the MIUR under grant  ... 
dblp:conf/nips/AlmanzaCLPR21 fatcat:a6bpwuqdibbeha2hbbwt7ld6uy

A Primal-Dual Algorithm for Online Non-uniform Facility Location [chapter]

Dimitris Fotakis
2005 Lecture Notes in Computer Science  
In the online version of Facility Location, the demand points arrive one at a time and must be irrevocably assigned to an open facility upon arrival.  ...  The objective is to minimize the sum of facility and assignment costs. We present a simple deterministic primal-dual algorithm for the general case of non-uniform facility costs.  ...  In Online Facility Location, the demand points arrive one at a time and must be irrevocably assigned to either an existing or a new facility upon arrival.  ... 
doi:10.1007/11573036_5 fatcat:6zihtaxqtbd6jbcyo7t3xpp5ma

A primal-dual algorithm for online non-uniform facility location

Dimitris Fotakis
2007 Journal of Discrete Algorithms  
In the online version of Facility Location, the demand points arrive one at a time and must be irrevocably assigned to an open facility upon arrival.  ...  The objective is to minimize the sum of facility and assignment costs. We present a simple deterministic primal-dual algorithm for the general case of non-uniform facility costs.  ...  In Online Facility Location, the demand points arrive one at a time and must be irrevocably assigned to either an existing or a new facility upon arrival.  ... 
doi:10.1016/j.jda.2006.03.001 fatcat:4bl3h2bbdnhwhbgcvebn6k4ecm

The Online Multi-Commodity Facility Location Problem [article]

Jannik Castenow, Björn Feldkord, Till Knollmann, Manuel Malatyali, Friedhelm Meyer auf der Heide
2020 arXiv   pre-print
On the one hand, we show that heterogeneity influences the competitive ratio by developing a lower bound on the competitive ratio for any randomized online algorithm of Ω(√(|S|)+log n/loglog n) that already  ...  Ravi and Sinha (SODA'04) introduced the model as the Multi-Commodity Facility Location Problem (MFLP) and considered it an offline optimization problem.  ...  To the best of our knowledge, no work has been done on an online variant of our problem so far. Our Results The rest of this paper is structured as follows.  ... 
arXiv:2005.08391v2 fatcat:4sh2wqlsfbbq3onvik6tmaduzy

Online and incremental algorithms for facility location

Dimitris Fotakis
2011 ACM SIGACT News  
In the online and incremental variants of Facility Location, the demands arrive one-by-one and must be assigned to an open facility upon arrival, without any knowledge about future demands.  ...  In this survey, we discuss the previous work on online and incremental algorithms for Facility Location.  ...  The potential of u i serves as an upper bound both on u i 's assignment cost and on how much u i can contribute to the opening cost of new facilities closer to it.  ... 
doi:10.1145/1959045.1959065 fatcat:3o7lzly7srf27jxluvw6r2a7lq

Learning Augmented Online Facility Location [article]

Dimitris Fotakis, Evangelia Gergatsouli, Themis Gouleakis, Nikolas Patris
2022 arXiv   pre-print
In Online Facility Location (OFL), demands arrive one-by-one in a metric space and must be (irrevocably) assigned to an open facility upon arrival, without any knowledge about future demands.  ...  consider the Online Facility Location problem under this framework.  ...  The algorithm decides whether to open a new facility f new and connect this point or connect it to an already open one.  ... 
arXiv:2107.08277v2 fatcat:fze3eo3czrgchaxvyftiaalrwu

On the Competitive Ratio for Online Facility Location [chapter]

Dimitris Fotakis
2003 Lecture Notes in Computer Science  
We consider the problem of Online Facility Location, where demands arrive online and must be irrevocably assigned to an open facility upon arrival.  ...  The objective is to minimize the sum of facility and assignment costs. We prove that the competitive ratio for Online Facility Location is Θ( log n log log n ).  ...  As a result, the upper bound of f on the potential accumulated by c * cannot be directly translated into an upper bound on the total assignment cost of the inner demands arriving in phase as in [16] .  ... 
doi:10.1007/3-540-45061-0_51 fatcat:2opqqzd5o5gxtintoikixmppyy

On the Competitive Ratio for Online Facility Location

Dimitris Fotakis
2007 Algorithmica  
We consider the problem of Online Facility Location, where demands arrive online and must be irrevocably assigned to an open facility upon arrival.  ...  The objective is to minimize the sum of facility and assignment costs. We prove that the competitive ratio for Online Facility Location is Θ( log n log log n ).  ...  As a result, the upper bound of f on the potential accumulated by c * cannot be directly translated into an upper bound on the total assignment cost of the inner demands arriving in phase as in [16] .  ... 
doi:10.1007/s00453-007-9049-y fatcat:6bhi74fgung6ncigyjom4qlaca

An improved lower bound for one-dimensional online unit clustering [article]

Jun Kawahara, Koji M. Kobayashi
2015 arXiv   pre-print
The task of an algorithm is to cover a new given point either by creating a new cluster and assigning it to the point, or by extending edges of an existing cluster created in past times.  ...  The online unit clustering problem was proposed by Chan and Zarrabi-Zadeh (WAOA2007 and Theory of Computing Systems 45(3), 2009), which is defined as follows: "Points" are given online in the d-dimensional  ...  Clustering problems are applied for various purposes such as information retrieval, data mining and facility location.  ... 
arXiv:1502.02422v1 fatcat:lr5ip65yqzb35fjwh6o3ywl5s4

Online Clustering on the Line with Square Cost Variable Sized Clusters

Gabriella Divéki
2013 Acta Cybernetica  
We present the first online algorithms for the solution of the problem. We describe algorithms for the strict and the flexible variant both for the online and semi-online versions.  ...  We also give lower bounds on the possible competitive ratio in all of the cases.  ...  In some of the online facility location models it is allowed to merge clusters or to re-assign points. Our results: We present the first online algorithms for the solution of the problem.  ... 
doi:10.14232/actacyb.21.1.2013.6 fatcat:nqv223syxzh55i4jogdjlochgy
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