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Journal of Systems Science and Complexity

, Volume 28, Issue 5, pp 1102–1114 | Cite as

Approximation algorithms for the priority facility location problem with penalties

  • Fengmin Wang
  • Dachuan XuEmail author
  • Chenchen Wu
Article
  • 161 Downloads

Abstract

This paper considers the priority facility location problem with penalties. The authors develop a primal-dual 3-approximation algorithm for this problem. Combining with the greedy augmentation procedure, the authors further improve the previous ratio 3 to 1.8526.

Keywords

Approximation algorithm facility location problem greedy augmentation primal-dual 

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References

  1. [1]
    Shmoys D B, Tardos É, and Aardal K I, Approximation algorithms for facility location problems, Proceedings of STOC, 1997, 265–274.Google Scholar
  2. [2]
    Li S, A 1.488-approximation algorithm for the uncapacitated facility location problem, Proceedings of ICALP, Part II, 2011, 77–88.Google Scholar
  3. [3]
    Guha S and Khuller S, Greedy strikes back: Improved facility location algorithms, Proceedings of SODA, 1998, 649–657.Google Scholar
  4. [4]
    Ageev A, Ye Y, and Zhang J, Improved combinatorial approximation algorithms for the k-level facility location problem, SIAM J. Discrete Math., 2003, 18: 207–217.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Charikar M and Guha S, Improved combinatorial algorithms for facility location problems, SIAM J. Comput., 2005, 34: 803–824.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Zhang J, Chen B, and Ye Y, A multiexchange local search algorithm for the capacitated facility location problem, Math. Oper. Res., 2005, 30: 389–403.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Zhang J, Approximating the two-level facility location problem via a quasi-greedy approach, Math. Program., 2006, 108: 159–176.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Zhang P, A new approximation algorithm for the k-facility location problem, Theor. Comput. Sci., 2007, 384: 126–135.CrossRefzbMATHGoogle Scholar
  9. [9]
    Chen X and Chen B, Approximation algorithms for soft-capacitated facility location in capacitated network design, Algorithmica, 2009, 53: 263–297.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Du D, Wang X, and Xu D, An approximation algorithm for the k-level capacitated facility location problem, J. Comb. Optim., 2010, 20: 361–368.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Shu J, An efficient greedy heuristic for warehouse-retailer network design optimization, Transport. Sci., 2010, 44: 183–192.CrossRefGoogle Scholar
  12. [12]
    Du D, Lu R, and Xu D, A primal-dual approximation algorithm for the facility location problem with submodular penalties, Algorithmica, 2012, 63: 191–200.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Charikar M, Khuller S, Mount D M, and Narasimhan G, Algorithms for facility location problems with outliers, Proceedings of SODA, 2001, 642–651.Google Scholar
  14. [14]
    Xu G and Xu J, An LP-rounding algorithm for approximating uncapacitated facility location problem with penalties, Inform. Process. Lett., 2005, 94: 119–123.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Xu G and Xu J, An improved approximation algorithm for uncapacitated facility location problem with penalties, J. Comb. Optim., 2008, 17: 424–436.CrossRefGoogle Scholar
  16. [16]
    Hayrapetyan A, Swamy C, and Tardos É, Network design for information networks, Proceedings of SODA, 2005, 933–942.Google Scholar
  17. [17]
    Chudak F A and Nagano K, Efficient solutions to relaxations of combinatorial problems with submodular penalties via the Lovász extension and non-smooth convex optimization, Proceedings of SODA, 2007, 79–88.Google Scholar
  18. [18]
    Ravi R and Sinha A, Multicommodity facility location, Proceedings of SODA, 2004, 342–349.Google Scholar
  19. [19]
    Mahdian M, Facility location and the analysis of algorithms through factor-revealing problems, Ph.D.’s degree thesis, Massachusetts Institute of Technology, Cambridge, MA, 2004.Google Scholar
  20. [20]
    Li G, Wang Z, and Wu C, Approximation algorithms for the stochastic priority facility location problem, Optimization, 2013, 62(7): 919–928.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Jain K and Vazirani V V, Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation, J. ACM, 2001, 48: 274–296.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.College of Applied SciencesBeijing University of TechnologyBeijingChina
  2. 2.College of ScienceTianjin University of TechnologyTianjinChina

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