research-article

Dynamic Facility Location via Exponential Clocks

Authors:

Ashkan Norouzi-Fard,

Ola SvenssonAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 13, Issue 2

Article No.: 21, Pages 1 - 20

https://doi.org/10.1145/2928272

Published: 07 February 2017 Publication History

Abstract

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 connects 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.

References

[1]

A. Anagnostopoulos, R. Bent, E. Upfal, and P. Van Hentenryck. 2004. A simple and deterministic competitive algorithm for online facility location. Inf. Comput. 194, 2 (2004), 175--202.

Digital Library

[2]

B. M. Anthony and A. Gupta. 2007. Infrastructure leasing problems. In Proceedings of the 12th International Conference on Integer Programming and Combinatorial Optimization (IPCO’07). 424--438.

Digital Library

[3]

V. Arya, N. Garg, R. Khandekar, A. Meyerson, K. Munagala, and V. Pandit. 2004. Local search heuristics for k-median and facility location problems. SIAM J. Comput. 33, 3 (2004), 544--562.

Digital Library

[4]

N. Buchbinder, S. Chen, and J. (Seffi) Naor. 2014. Competitive analysis via regularization. In Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’14). 436--444.

Digital Library

[5]

N. Buchbinder, J. (Seffi) Naor, and R. Schwartz. 2013. Simplex partitioning via exponential clocks and the multiway cut problem. In Proceedings of the 45th Annual ACM Symposium on Theory of Computing (STOC’13). 535--544.

Digital Library

[6]

J. Byrka and K. Aardal. 2010. An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. SIAM J. Comput. 39, 6 (2010), 2212--2231.

[7]

M. Charikar and S. Guha. 2005. Improved combinatorial algorithms for facility location problems. SIAM J. Comput. 34, 4 (2005), 803--824.

Digital Library

[8]

F. A. Chudak and D. B. Shmoys. 2004. Improved approximation algorithms for the uncapacitated facility location problem. SIAM J. Comput. 33, 1 (2004), 1--25.

Digital Library

[9]

G. Divéki and C. Imreh. 2011. Online facility location with facility movements. Centr. Eur. J. Operat. Res. 19, 2 (2011), 191--200.

[10]

D. Eisenstat, C. Mathieu, and N. Schabanel. 2014. Facility location in evolving metrics. In Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP’14). 459--470.

[11]

D. Fotakis. 2006. Incremental algorithms for facility location and k-median. Theor. Comput. Sci. 361, 2--3 (2006), 275--313.

Digital Library

[12]

D. Fotakis. 2008. On the competitive ratio for online facility location. Algorithmica 50, 1 (2008), 1--57.

Digital Library

[13]

D. Fotakis. 2011. Online and incremental algorithms for facility location. SIGACT News 42, 1 (2011), 97--131.

Digital Library

[14]

K. Jain, M. Mahdian, E. Markakis, A. Saberi, and V. V. Vazirani. 2003. Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. J. ACM 50, 6 (2003), 795--824.

Digital Library

[15]

K. Jain, M. Mahdian, and A. Saberi. 2002. A new greedy approach for facility location problems. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC’02). 731--740.

Digital Library

[16]

K. Jain and V. V. Vazirani. 2001. Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation. J. ACM 48, 2 (2001), 274--296.

Digital Library

[17]

S. Li. 2013. A 1.488 approximation algorithm for the uncapacitated facility location problem. Inform. Comput. 222 (2013), 45--58.

Digital Library

[18]

J. Lin and J. S. Vitter. 1992. Approximation algorithms for geometric median problems. Inform. Process. Lett. 44, 5 (1992), 245--249.

Digital Library

[19]

A. Meyerson. 2001. Online facility location. In Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS’01). 426--431.

Digital Library

[20]

C. Nagarajan and D. P. Williamson. 2008. Offline and online facility leasing. In Proceedings of the 13th International Conference on Integer Programming and Combinatorial Optimization (IPCO’08). 303--315. http://dl.acm.org/citation.cfm?id=1788814.1788842.

Digital Library

[21]

M. Newman. 2003. The structure and function of complex networks. SIAM Rev. 45, 2 (2003), 167--256.

Digital Library

[22]

R. Pastor-Satorras and A. Vespignani. 2001. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 14 (2001), 3200--3203.

[23]

D. B. Shmoys, E. Tardos, and K. Aardal. 1997. Approximation algorithms for facility location problems (extended abstract). In Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC’97). 265--274.

Digital Library

[24]

J. Stehlé, N. Voirin, A. Barrat, C. Cattuto, L. Isella, J.-F. Pinton, M. Quaggiotto, W. Van den Broeck, C. Régis, B. Lina, and P. Vanhems. 2011. High-resolution measurements of face-to-face contact patterns in a primary school. PLoS ONE 6, 8 (2011), e23176.

[25]

C. Tantipathananandh, T. Berger-Wolf, and D. Kempe. 2007. A framework for community identification in dynamic social networks. In Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’07). 717--726.

Digital Library

Cited By

Christou DSkoulakis SCevher VOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Efficient online clustering with moving costsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667223(25325-25364)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667223
Bampis ECella CEscoffier BRocco MTeiller A(2023)Target-based computer-assisted orchestration: Complexity and approximation algorithmsEuropean Journal of Operational Research10.1016/j.ejor.2022.05.008304:3(926-938)Online publication date: Feb-2023
https://doi.org/10.1016/j.ejor.2022.05.008
Bernardini GLindermayr AMarchetti-Spaccamela AMegow NStougie LSweering MKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)A universal error measure for input predictions applied to online graph problemsProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3600500(3178-3190)Online publication date: 28-Nov-2022
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Index Terms

Dynamic Facility Location via Exponential Clocks
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Facility location and clustering

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 13, Issue 2

Special Issue on SODA'15 and Regular Papers

April 2017

316 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3040971

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2017 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 07 February 2017

Accepted: 01 April 2016

Revised: 01 April 2016

Received: 01 April 2015

Published in TALG Volume 13, Issue 2

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Yonsei University New Faculty Seed
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National Research Foundation of Korea (NRF)
Korea government (MSIP)

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Cited By

Christou DSkoulakis SCevher VOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Efficient online clustering with moving costsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667223(25325-25364)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667223
Bampis ECella CEscoffier BRocco MTeiller A(2023)Target-based computer-assisted orchestration: Complexity and approximation algorithmsEuropean Journal of Operational Research10.1016/j.ejor.2022.05.008304:3(926-938)Online publication date: Feb-2023
https://doi.org/10.1016/j.ejor.2022.05.008
Bernardini GLindermayr AMarchetti-Spaccamela AMegow NStougie LSweering MKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)A universal error measure for input predictions applied to online graph problemsProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3600500(3178-3190)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3600500
Bampis EChristou DEscoffier BKononov AThang N(2022)A Simple Rounding Scheme for Multistage OptimizationTheoretical Computer Science10.1016/j.tcs.2022.01.009Online publication date: Jan-2022
https://doi.org/10.1016/j.tcs.2022.01.009
Deng SLi JRabani Y(2022)Approximation algorithms for clustering with dynamic pointsJournal of Computer and System Sciences10.1016/j.jcss.2022.07.001130:C(43-70)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1016/j.jcss.2022.07.001
Bampis EEscoffier BTeiller A(2022)Multistage knapsackJournal of Computer and System Sciences10.1016/j.jcss.2022.01.002126(106-118)Online publication date: Jun-2022
https://doi.org/10.1016/j.jcss.2022.01.002
Fotakis DKavouras LZakynthinou L(2021)Online Facility Location in Evolving MetricsAlgorithms10.3390/a1403007314:3(73)Online publication date: 25-Feb-2021
https://doi.org/10.3390/a14030073
Fotakis DKavouras LKostopanagiotis PLazos PSkoulakis SZarifis N(2021)Reallocating multiple facilities on the lineTheoretical Computer Science10.1016/j.tcs.2021.01.028858(13-34)Online publication date: Feb-2021
https://doi.org/10.1016/j.tcs.2021.01.028
Bampis EEscoffier BSchewior KTeiller A(2021)Online Multistage Subset Maximization ProblemsAlgorithmica10.1007/s00453-021-00834-783:8(2374-2399)Online publication date: 1-Aug-2021
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Bampis EEscoffier BKononov A(2020)LP-Based Algorithms for Multistage Minimization ProblemsApproximation and Online Algorithms10.1007/978-3-030-80879-2_1(1-15)Online publication date: 9-Sep-2020
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