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Journal of Combinatorial Optimization

, Volume 35, Issue 2, pp 493–511 | Cite as

An approximation algorithm for soft capacitated k-facility location problem

  • Yanjun Jiang
  • Dachuan Xu
  • Donglei Du
  • Chenchen Wu
  • Dongmei Zhang
Article
  • 146 Downloads

Abstract

We present a \((20+{5}/{n})\)-approximation algorithm for the non-uniform soft capacitated k-facility location problem, violating the capacitated constrains by no more than a factor of 25. The main technique is based on the primal–dual algorithm for the soft capacitated facility location problem, and the exploitation of the combinatorial structure of the fractional solution for the soft capacitated k-facility location problem.

Keywords

Approximation algorithm Soft capacitated k-facility location problem Primal–dual scheme 

Notes

Acknowledgements

The research of the second author is supported by NSFC (No. 11531014). The third author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 283106. The fourth author’s research is supported by NSFC (No. 11501412). The fifth author’s research is supported by Higher Educational Science and Technology Program of Shandong Province (No. J15LN22).

References

  1. Aggarwal A, Anand L, Bansal M, Garg N, Gupta N, Gupta S, Jain S (2010) A 3-approximation for facility location with uniform capacities. In: Proceedings of IPCO, pp 149–162Google Scholar
  2. Aardal K, van den Berg PL, Gijswijt D, Li S (2015) Approximation algorithms for hard capacitated \(k\)-facility location problems. Eur J Op Res 242:358–368MathSciNetCrossRefMATHGoogle Scholar
  3. Ageev A, Ye Y, Zhang J (2004) Improved combinatorial approximation algorithm for the \(k\)-level facility location problem. SIAM J Discrete Math 18:207–217MathSciNetCrossRefMATHGoogle Scholar
  4. Byrka J, Fleszar K, Rybicki B, Spoerhase J (2015) Bi-factor approximation algorithms for hard capacitated \(k\)-median problems. In: Proceedings of SODA, pp 722–736Google Scholar
  5. Byrka J, Pensyl T, Rybicki B, Srinivasan A, Trinh K (2015) An improved approximation for \(k\)-median and positive correlation in budgeted optimization. In: Proceedings of SODA, pp 737–756Google Scholar
  6. Byrka J, Rybicki B, Uniyal S (2016) An approximation algorithm for uniform capacitated \(k\)-median problem with \(1+\epsilon \) capacity violation. In: Proceedings of IPCO, pp 262-274Google Scholar
  7. Chen X, Chen B (2009) Approximation algorithm for soft-capacitated facility location in capacitated network design. Algorithmica 53:263–297MathSciNetCrossRefMATHGoogle Scholar
  8. Charika M, Guha S, Tardos É, Shmoys D (1999) A constant-factor approximation algorithm for the \(k\)-median problem (extened abstract). In: Proceedings of STOC, pp 1–10Google Scholar
  9. Chuzhoy J, Rabani Y (2005) Approximating \(k\)-median with non-uniform capacities. In: Proceedings of SODA, pp 952–958Google Scholar
  10. Du D, Lu R, Xu D (2012) A primal–dual approximation algorithm for the facility location problem with submodular penalties. Algorithmica 63:191–200MathSciNetCrossRefMATHGoogle Scholar
  11. Gijswijt D, Li S (2013) Approximation algorithms for the capacitated \(k\)-facility location problems. arXiv:1311.4759
  12. Guha S, Khuller S (1999) Greedy strikes back: improved facility location algorithms. J Algorithms 31:228–248MathSciNetCrossRefMATHGoogle Scholar
  13. Guha S, Meyerson A, Munagala, K (2000) Hierarchical placement and network design problems. In: Proceedings of FOCS, pp 603–612Google Scholar
  14. Hochbaum D (1997) Approximation algorithms for NP-hard problems. PWS Publishing Company, BostonMATHGoogle Scholar
  15. 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 48:274–296MathSciNetCrossRefMATHGoogle Scholar
  16. Kuehn A, Hamburger M (1963) A heuristic program for locating warehouses. Manage Sci 9:643–666CrossRefGoogle Scholar
  17. Li S (2011) A \(1.488\)-approximation algorithm for the uncapacitated facility location problem. In: Proceedings of ICALP, Part 2, pp 77–88Google Scholar
  18. Li S (2015) On uniform capacitated \(k\)-median beyond the natural LP relaxation. In: Proceedings of SODA, pp 696–707Google Scholar
  19. Li S (2016) Approximating capacitated \(k\)-median with \((1+\epsilon )k\) open facilities. In: Proceedings of SODA, pp 786–796Google Scholar
  20. Love R, Morris J, Wesolowsky G (1988) Facilities location: models and methods. North-Holland, New YorkMATHGoogle Scholar
  21. Li S, Svensson O (2013) Approximating \(k\)-median via pseudo-approximation. In: Proceedings of STOC, pp 901–910Google Scholar
  22. Mahdian M, Ye Y, Zhang J (2006) Approximation algorithm for metric facility location problem. SIAM J Comput 36:411–432MathSciNetCrossRefMATHGoogle Scholar
  23. Qiu L, Padmanabhan V, Voelker G (2001) On the placement of web server replicas. Proceedings of INFOCOM, vol. 3, pp 1587–1596Google Scholar
  24. Shmoys D, Tardös É, Aardal K (1997) Approximation algorithm for facility location problems. In: Proceedings of STOC, pp 265–274Google Scholar
  25. Zhang P (2007) A new approximation algorithm for the \(k\)-facility location problem. Theor Comput Sci 384:126–135MathSciNetCrossRefMATHGoogle Scholar
  26. Zhang J, Chen B, Ye Y (2005) A multiexchange local search algorithm for the capacitated facility location problem. Math Op Res 30:389–403MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Yanjun Jiang
    • 1
  • Dachuan Xu
    • 1
  • Donglei Du
    • 2
  • Chenchen Wu
    • 3
  • Dongmei Zhang
    • 4
  1. 1.Department of Information and Operations Research, College of Applied SciencesBeijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.Faculty of Business AdministrationUniversity of New BrunswickFrederictonCanada
  3. 3.College of ScienceTianjin University of TechnologyTianjinPeople’s Republic of China
  4. 4.School of Computer Science and TechnologyShandong Jianzhu UniversityJinanPeople’s Republic of China

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