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An approximation algorithm for soft capacitated k-facility location problem

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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.

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References

  • 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 149–162

  • Aardal K, van den Berg PL, Gijswijt D, Li S (2015) Approximation algorithms for hard capacitated \(k\)-facility location problems. Eur J Op Res 242:358–368

    Article  MathSciNet  MATH  Google Scholar 

  • Ageev A, Ye Y, Zhang J (2004) Improved combinatorial approximation algorithm for the \(k\)-level facility location problem. SIAM J Discrete Math 18:207–217

    Article  MathSciNet  MATH  Google Scholar 

  • Byrka J, Fleszar K, Rybicki B, Spoerhase J (2015) Bi-factor approximation algorithms for hard capacitated \(k\)-median problems. In: Proceedings of SODA, pp 722–736

  • 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 737–756

  • 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 262-274

  • Chen X, Chen B (2009) Approximation algorithm for soft-capacitated facility location in capacitated network design. Algorithmica 53:263–297

    Article  MathSciNet  MATH  Google Scholar 

  • 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 1–10

  • Chuzhoy J, Rabani Y (2005) Approximating \(k\)-median with non-uniform capacities. In: Proceedings of SODA, pp 952–958

  • Du D, Lu R, Xu D (2012) A primal–dual approximation algorithm for the facility location problem with submodular penalties. Algorithmica 63:191–200

    Article  MathSciNet  MATH  Google Scholar 

  • Gijswijt D, Li S (2013) Approximation algorithms for the capacitated \(k\)-facility location problems. arXiv:1311.4759

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

    Article  MathSciNet  MATH  Google Scholar 

  • Guha S, Meyerson A, Munagala, K (2000) Hierarchical placement and network design problems. In: Proceedings of FOCS, pp 603–612

  • Hochbaum D (1997) Approximation algorithms for NP-hard problems. PWS Publishing Company, Boston

    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 48:274–296

    Article  MathSciNet  MATH  Google Scholar 

  • Kuehn A, Hamburger M (1963) A heuristic program for locating warehouses. Manage Sci 9:643–666

    Article  Google Scholar 

  • Li S (2011) A \(1.488\)-approximation algorithm for the uncapacitated facility location problem. In: Proceedings of ICALP, Part 2, pp 77–88

  • Li S (2015) On uniform capacitated \(k\)-median beyond the natural LP relaxation. In: Proceedings of SODA, pp 696–707

  • Li S (2016) Approximating capacitated \(k\)-median with \((1+\epsilon )k\) open facilities. In: Proceedings of SODA, pp 786–796

  • Love R, Morris J, Wesolowsky G (1988) Facilities location: models and methods. North-Holland, New York

    MATH  Google Scholar 

  • Li S, Svensson O (2013) Approximating \(k\)-median via pseudo-approximation. In: Proceedings of STOC, pp 901–910

  • Mahdian M, Ye Y, Zhang J (2006) Approximation algorithm for metric facility location problem. SIAM J Comput 36:411–432

    Article  MathSciNet  MATH  Google Scholar 

  • Qiu L, Padmanabhan V, Voelker G (2001) On the placement of web server replicas. Proceedings of INFOCOM, vol. 3, pp 1587–1596

  • Shmoys D, Tardös É, Aardal K (1997) Approximation algorithm for facility location problems. In: Proceedings of STOC, pp 265–274

  • Zhang P (2007) A new approximation algorithm for the \(k\)-facility location problem. Theor Comput Sci 384:126–135

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang J, Chen B, Ye Y (2005) A multiexchange local search algorithm for the capacitated facility location problem. Math Op Res 30:389–403

    Article  MathSciNet  MATH  Google Scholar 

Download references

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).

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Authors and Affiliations

  1. 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

    Yanjun Jiang & Dachuan Xu

  2. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

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

    Chenchen Wu

  4. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, People’s Republic of China

    Dongmei Zhang

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  1. Yanjun Jiang
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  2. Dachuan Xu
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  3. Donglei Du
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  4. Chenchen Wu
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  5. Dongmei Zhang
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Correspondence to Dongmei Zhang.

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Jiang, Y., Xu, D., Du, D. et al. An approximation algorithm for soft capacitated k-facility location problem. J Comb Optim 35, 493–511 (2018). https://doi.org/10.1007/s10878-017-0192-3

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