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Approximation algorithm for squared metric two-stage stochastic facility location problem

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Abstract

In this paper, we consider a variant of the classical uncapacitated facility location problem, so-called squared metric two-stage stochastic facility location problem (SM-2-SFLP) which can treat the uncertainty of the set of clients and facility costs. We assume that the connection cost is squared metric, a variant of the metric case which is widely researched. We give a new 0–1 integer linear programming for SM-2-SFLP. Based on the new formulation, we apply two known algorithms to SM-2-SFLP, and analyze the approximation ratio and per-scenario bound respectively.

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References

  • Byrka J, Srinivasan A (2018) Approximation algorithms for stochastic and risk-averse optimization. SIAM J Discrete Math 32(1):44–63

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Chudak FA, Shmoys DB (2003) Improved approximation algorithms for the uncapacitated facility location problem. SIAM J Comput 33(1):1–25

    Article  MathSciNet  MATH  Google Scholar 

  • Fernandes CG, Meira LAA, Miyazawa FK, Pedrosa LLC (2015) A systematic approach to bound factor-revealing LPs and its application to the metric and squared metric facility location problems. Math Program 153(2):655–685

    Article  MathSciNet  MATH  Google Scholar 

  • Guha S, Khuller S (1999) Greedy strikes back: Improved facility location algorithms. J Algorithms 31(1):228–248

    Article  MathSciNet  MATH  Google Scholar 

  • Jain K, Vazirani VV (2001) Approximation algorithms for metric facility location and \(k\)-median problems using the primal-dual schema and Lagrangian relaxation. J ACM 48(2):274–296

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Korupolu MR, Plaxton CG, Rajaraman R (2000) Analysis of a local search heuristic for facility location problems. J Algorithms 37(1):146–188

    Article  MathSciNet  MATH  Google Scholar 

  • Li S (2013) A 1.488 approximation algorithm for the uncapacitated facility location problem. Inf Comput 222:45–58

    Article  MathSciNet  MATH  Google Scholar 

  • Ravi R, Sinha A (2006) Hedging uncertainty: approximation algorithms for stochastic optimization problems. Math Program 108(1):97–114

    Article  MathSciNet  MATH  Google Scholar 

  • Shao J, Xu D (2013) An approximation algorithm for the risk-adjusted two-stage stochastic facility location problem with penalties. J Oper Res Soc China 1(3):339–346

    Article  MATH  Google Scholar 

  • Shmoys DB, Tardos É, Aardal K (1997) Approximation algorithms for facility location problems. In: Proceedings of the 29th annual ACM symposium on theory of computing, pp 265–274

  • Sviridenko M (2002) An improved approximation algorithm for the metric uncapacitated facility location problem. In: Proceedings of the 9th international conference on integer programming and combinatorial optimization, pp 240–257

  • Swamy C (2004) Approximation algorithms for clustering problems. Ph.D. thesis. Cornell University

  • Wu C, Xu D, Shu J (2013) An approximation algorithm for the stochastic fault-tolerant facility location problem. J Oper Res Soc China 1(4):511–522

    Article  MATH  Google Scholar 

  • Wu C, Du D, Xu D (2015) An improved per-scenario bound for the two-stage stochastic facility location problem. Sci China Math 58(1):213–220

    Article  MathSciNet  MATH  Google Scholar 

  • Ye Y, Zhang J (2006) An approximation algorithm for the dynamic facility location problem. In: Combinatorial optimization in communication networks. Springer, Boston, MA, pp 623–637

    MATH  Google Scholar 

Download references

Acknowledgements

The work of the first author is supported by the National Key Research and Development Program of China (Grant No. 2018YFF0213304). The work of the second author is supported by the Higher Educational Science and Technology Program of Shandong Province (Grant No. J17KA171). The work of the third author is supported by the National Natural Science Foundation of China (Grant Nos. 61433012, U1435215). The work of the fourth author is supported by the National Natural Science Foundation of China (Grant No. 11501412). The fifth author is supported by the National Natural Science Foundation of China (Grant Nos. 11531014, 11871081).

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Authors and Affiliations

  1. Beijing Key Laboratory of Green Building and Energy Saving Technology, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, People’s Republic of China

    Jin Zhang

  2. Beijing Key Laboratory of Control Technology for City Toxic and Combustible Major Hazards, Beijing Municipal Institute of Labour Protection, Taoranting Street No. 55, Xicheng District, Beijing, 100054, People’s Republic of China

    Jin Zhang

  3. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Min Li

  4. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, 1068 Xueyuan Avenue, Shenzhen University Town, Shenzhen, 518055, People’s Republic of China

    Yishui Wang

  5. College of Science, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Chenchen Wu

  6. Department of Information and Operations Research, College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, People’s Republic of China

    Dachuan Xu

Authors
  1. Jin Zhang
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  2. Min Li
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  3. Yishui Wang
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  4. Chenchen Wu
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  5. Dachuan Xu
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Corresponding author

Correspondence to Min Li.

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Zhang, J., Li, M., Wang, Y. et al. Approximation algorithm for squared metric two-stage stochastic facility location problem. J Comb Optim 38, 618–634 (2019). https://doi.org/10.1007/s10878-019-00404-2

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  • DOI: https://doi.org/10.1007/s10878-019-00404-2

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