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A Greedy Facility Location Algorithm Analyzed Using Dual Fitting [chapter]

Mohammad Mahdian, Evangelos Markakis, Amin Saberi, Vijay Vazirani
2001 Lecture Notes in Computer Science  
We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861.  ...  We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions.  ...  Mohammad Ghodsi, Computer Engineering Department, Sharif University of Technology, for introducing them to the facility location problem. We would also like to thank Nisheet K.  ... 
doi:10.1007/3-540-44666-4_16 fatcat:bsnkbjkmc5ey3ah3qor2bqumvu

Page 3082 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
, Evangelos (1-GAIT-CC; Atlanta, GA); Saberi, Amin (1-GAIT-CC; Atlanta, GA); Vazirani, Vijay (1-GAIT-CC; Atlanta, GA) A greedy facility location algorithm analyzed using dual fitting.  ...  Summary: “We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861  ... 

Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP

Kamal Jain, Mohammad Mahdian, Evangelos Markakis, Amin Saberi, Vijay V. Vazirani
2003 Journal of the ACM  
This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem.  ...  In this article, we will formalize the method of dual fitting and the idea of factor-revealing LP.  ...  We would also like to thank Sudipto Guha for informing us of the OR library. Finally, we thank the anonymous referees for their comments.  ... 
doi:10.1145/950620.950621 fatcat:2surabim5fgklgm7qmdc3endlm

Greedy Facility Location Algorithms Analyzed using Dual Fitting with Factor-Revealing LP [article]

Kamal Jain and Mohammad Mahdian and Evangelos Markakis and Amin Saberi and Vijay V. Vazirani
2002 arXiv   pre-print
This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem.  ...  In this paper, we will formalize the method of dual fitting and the idea of factor-revealing LP.  ...  Using this combination we analyze two greedy algorithms for the metric uncapacitated facility location problem.  ... 
arXiv:cs/0207028v1 fatcat:7dcegvj45nhzbmgyfp3kfbtikq

A new greedy approach for facility location problems

Kamal Jain, Mohammad Mahdian, Amin Saberi
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem.  ...  In this article, we will formalize the method of dual fitting and the idea of factor-revealing LP.  ...  We would also like to thank Sudipto Guha for informing us of the OR library. Finally, we thank the anonymous referees for their comments.  ... 
doi:10.1145/509907.510012 dblp:conf/stoc/JainMS02 fatcat:xl36yca6ujeihd6ksiggwx2ciu

A new greedy approach for facility location problems

Kamal Jain, Mohammad Mahdian, Amin Saberi
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem.  ...  In this article, we will formalize the method of dual fitting and the idea of factor-revealing LP.  ...  We would also like to thank Sudipto Guha for informing us of the OR library. Finally, we thank the anonymous referees for their comments.  ... 
doi:10.1145/510008.510012 fatcat:4atv627uhzfrpaydojz2yhodhm

Strategyproof cost-sharing mechanisms for set cover and facility location games

Nikhil R. Devanur, Milena Mihail, Vijay V. Vazirani
2003 Proceedings of the 4th ACM conference on Electronic commerce - EC '03  
ACKNOWLEDGEMENTS We would like to thank Aranyak Mehta and Amin Saberi for useful discussions.  ...  The approximation guarantee is then obtained using dual fitting.  ...  As in the set cover problem, the mechanism uses the underlying greedy algorithm in [7, 13] . Consider the following IP-formulation of the facility location problem.  ... 
doi:10.1145/779928.779942 dblp:conf/sigecom/DevanurMV03 fatcat:trchx5v6vrhn3hcohjt743xn7e

Strategyproof cost-sharing mechanisms for set cover and facility location games

Nikhil R. Devanur, Milena Mihail, Vijay V. Vazirani
2005 Decision Support Systems  
ACKNOWLEDGEMENTS We would like to thank Aranyak Mehta and Amin Saberi for useful discussions.  ...  The approximation guarantee is then obtained using dual fitting.  ...  As in the set cover problem, the mechanism uses the underlying greedy algorithm in [7, 13] . Consider the following IP-formulation of the facility location problem.  ... 
doi:10.1016/j.dss.2004.08.004 fatcat:54th4td5nbd6fmsiytnbyescti

Combinatorial Interpretations of Dual Fitting and Primal Fitting [chapter]

Ari Freund, Dror Rawitz
2004 Lecture Notes in Computer Science  
We use our second framework to design an approximation algorithm for the multiple metric uncapacitated facility location problem.  ...  We demonstrate the frameworks by presenting alternative analyses to the greedy algorithm for the set cover problem, and to known algorithms for the metric uncapacitated facility location problem.  ...  The dual fitting method was (implicitly) used previously to analyze the greedy H n -approximation algorithm for set cover [18, 10] .  ... 
doi:10.1007/978-3-540-24592-6_11 fatcat:4q6v3qaj7bb2dknta7i4wnujvu

Approximating the two-level facility location problem via a quasi-greedy approach

Jiawei Zhang
2006 Mathematical programming  
We propose a quasi-greedy algorithm for approximating the classical uncapacitated 2-level facility location problem (2-LFLP).  ...  Another feature of our algorithm is that it combines the technique of randomized rounding with that of dual fitting.  ...  Our algorithm and analysis combine the technique of randomized rounding with that of dual fitting.  ... 
doi:10.1007/s10107-006-0704-x fatcat:ntg5uh3ldnhtlfw4rny6s4zhqa

Parallel approximation algorithms for facility-location problems

Guy E. Blelloch, Kanat Tangwongsan
2010 Proceedings of the 22nd ACM symposium on Parallelism in algorithms and architectures - SPAA '10  
Our starting point is a small, but diverse, subset of results in approximation algorithms for facility-location problems, with a primary goal of developing techniques for devising their efficient parallel  ...  This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including NC and RNC algorithms for (metric) facility location, k-center, k-median, and  ...  FACILITY LOCATION: GREEDY The greedy scheme underlies an exceptionally simple algorithm for facility location, due to Jain et al. [18] .  ... 
doi:10.1145/1810479.1810535 dblp:conf/spaa/BlellochT10 fatcat:b57sj7o7hbhlph35lzq7gklwju

Online Network Design Algorithms via Hierarchical Decompositions [article]

Seeun Umboh
2014 arXiv   pre-print
In a sense, our work brings together two of the main approaches to online network design. The first uses greedy-like algorithms and analyzes them using dual-fitting.  ...  Our approach uses deterministic greedy-like algorithms but analyzes them via HST embeddings of the terminals.  ...  Acknowledgements The author is very grateful to Shuchi Chawla and Mohit Singh for helpful discussions and to the anonymous referees for their useful comments.  ... 
arXiv:1410.4240v1 fatcat:gmy6ciytaffcvhdpgfpkzsjxvi

Online Network Design Algorithms via Hierarchical Decompositions [chapter]

Seeun Umboh
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
In a sense, our work brings together two of the main approaches to online network design. The first uses greedy-like algorithms and analyzes them using dual-fitting.  ...  Our approach uses deterministic greedy-like algorithms but analyzes them via HST embeddings of the terminals.  ...  Acknowledgements The author is very grateful to Shuchi Chawla and Mohit Singh for helpful discussions and to the anonymous referees for their useful comments.  ... 
doi:10.1137/1.9781611973730.91 dblp:conf/soda/Umboh15 fatcat:x2krvj3n5fay7drisufa4vjp3u

Improved Combinatorial Algorithms for Facility Location Problems

Moses Charikar, Sudipto Guha
2005 SIAM journal on computing (Print)  
Combining greedy improvement and cost scaling with a recent primal-dual algorithm for facility location due to Jain and Vazirani, we get an approximation ratio of 1.853 inÕ(n 3 ) time.  ...  Further, combined with the best known LP-based algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving 1.728.  ...  We would also like to thank the referees for helping us improve the presentation of this manuscript significantly.  ... 
doi:10.1137/s0097539701398594 fatcat:7jsd7mhafveqjcwzbd2sixuqwe

A systematic approach to bound factor-revealing LPs and its application to the metric and squared metric facility location problems

Cristina G. Fernandes, Luis A. A. Meira, Flávio K. Miyazawa, Lehilton L. C. Pedrosa
2014 Mathematical programming  
We use UPFRPs in the dual-fitting analysis of the primal-dual algorithms for both the SMFLP and the MFLP, improving some of the previous analysis for the MFLP. ⋆  ...  We apply this technique to the Metric Facility Location Problem (MFLP) and to a generalization where the distance function is a squared metric.  ...  In [12] , a factor-revealing linear program is used to analyze Algorithm A3(δ) using a somewhat different, but equivalent, greedy augmentation procedure.  ... 
doi:10.1007/s10107-014-0821-x fatcat:ocacnzd63jgm5gr54miuvfcyw4
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