Movatterモバイル変換


[0]ホーム

URL:


Skip to main content

Advertisement

Springer Nature Link
Log in

A Primal-Dual Approximation Algorithm for thek-Level Stochastic Facility Location Problem

  • Conference paper

Part of the book series:Lecture Notes in Computer Science ((LNISA,volume 6124))

Included in the following conference series:

  • 744Accesses

  • 3Citations

Abstract

We present acombinatorial primal-dual 7-approximation algorithm for thek-level stochastic facility location problem, the stochastic counterpart of the standardk-level facility location problem. This approximation ratio is slightly worse than that of the primal-dual 6-approximation for the standardk-level facility location problem [3] because of the extra stochastic assumption. This new result complements the recentnon-combinatorial 3-approximation algorithm for the same problem by Wang et al [21].

This is a preview of subscription content,log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide -see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aardal, K.I., Chudak, F., Shmoys, D.B.: A 3-approximation algorithm for thek-level uncapacitated facility location problem. Information Processing Letters 72, 161–167 (1999)

    Article MATH MathSciNet  Google Scholar 

  2. Ageev, A., Ye, Y., Zhang, J.: Improved combinatorial apporximation algorithms for thek-level facility location problem. SIAM Journal on Discrete Mathematics 18(1), 207–217 (2004)

    Article MATH MathSciNet  Google Scholar 

  3. Bumb, A., Kern, W.: A simple dual ascent algorithm for the multilevel facility location problem. In: Proceedings of APPROX-RANDOM, pp. 55–63 (2001)

    Google Scholar 

  4. Byrka, J., Aardal, K.I.: An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. SIAM Journal on Computing (to appear)

    Google Scholar 

  5. Chen, X., Chen, B.: Approximation algorithms for soft-capacitated facility location in capacitated network design. Algorithmica 53(3), 263–297 (2007)

    Article  Google Scholar 

  6. Chudak, F., Shmoys, D.B.: Improved approxiamtion algorithms for the uncapaciteted facility location problem. SIAM Journal on Computing 33(1), 1–25 (2003)

    Article MATH MathSciNet  Google Scholar 

  7. Gabor, A.F., van Ommeren, J.-K.C.W.: A new approximation algorithm for the multilevel facility location problem. Discrete Applied Mathematics 158(5-6), 453–460 (2010)

    Article MATH MathSciNet  Google Scholar 

  8. Guha, S., Khuller, S.: Greedy strike back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)

    Article MATH MathSciNet  Google Scholar 

  9. Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Greedy facility location algorithm analyzed using dual fitting with factor-revealing LP. Jounal of the ACM 50, 795–824 (2003)

    Article MathSciNet  Google Scholar 

  10. Jain, K., Vazirani, V.V.: Approximation algorithms for metric facility location andk-median problems using the primal-dual schema and Lagrangian relaxation. Journal of the ACM 48, 274–296 (2001)

    Article MATH MathSciNet  Google Scholar 

  11. Mahdian, M.: Facility location and the analysis of algorithms through factor-revealing programs, Ph. D. thesis, MIT, Cambridge, MA (2004)

    Google Scholar 

  12. Mahdian, M., Ye, Y., Zhang, J.: Approximation algorithms for metric facility location problems. SIAM Journal on Computing 36(2), 411–432 (2006)

    Article MATH MathSciNet  Google Scholar 

  13. Ravi, R., Sinha, A.: Hedging uncertainty: approximation algorithhms for stochastic optimization problems. Mathematical Programming 108, 97–114 (2006)

    Article MATH MathSciNet  Google Scholar 

  14. Schrijver, A.: Combinatorial optimization: Polyhedra and Efficiency. In: Algorithms and Combinatorics, vol. 24(A). Springer, New York (2003)

    Google Scholar 

  15. Shmoys, D.B., Swamy, C.: An approximation scheme for stochastic linear programming and its application to stochastic integer programs. Journal of the ACM 53, 978–1012 (2006)

    Article MathSciNet  Google Scholar 

  16. Shmoys, D.B., Tardös, E., Aardal, K.I.: Approximation algorithms for facility location problems. In: Proceedings of STOC, pp. 265–274 (1997)

    Google Scholar 

  17. Shu, J.: An efficient greedy heuristic for warehouse-retailer network design optimization. Transportation Science, doi:10.1287/trsc.1090.0302

    Google Scholar 

  18. Shu, J., Ma, Q., Li, S.: Integrated location and two-echelon inventory network design under uncertainty. Annals of Operations Research, doi:10.1007/s10479-010-0732-z

    Google Scholar 

  19. Shu, J., Teo, C.P., Max Shen, Z.J.: Stochastic transportation-inventory network design problem. Operations Research 53, 48–60 (2005)

    Article MATH MathSciNet  Google Scholar 

  20. Srinivasan, A.: Approximation algorithms for stochastic and risk-averse optimization. In: Proceedings of SODA, pp. 1305–1313 (2007)

    Google Scholar 

  21. Wang, Z., Du, D., Gabor, A., Xu, D.: An approximation algorithm for thek-level stochastic facility location problem. Operations Research Letters, doi:10.1016/j.orl.2010.04.010

    Google Scholar 

  22. Ye, Y., Zhang, J.: An approximation algorithm for the dynamic facility location problem. In: Combinatorial Optimization in Communication Networks, pp. 623–637. Kluwer Academic Publishers, Dordrecht (2005)

    Google Scholar 

  23. Zhang, J.: Approximating the two-level facility location problem via a quasi-greedy approach. Mathematical Programming 108, 159–176 (2006)

    Article MATH MathSciNet  Google Scholar 

  24. Zhang, J., Chen, B., Ye, Y.: A multiexchange local search algorithm for the capacitated facility location problem. Mathematics of Operations Research 30(2), 389–403 (2005)

    Article MATH MathSciNet  Google Scholar 

  25. Zhang, P.: A new approximation algorithm for thek-facility location problem. Theoretical Computer Science 384(1), 126–135 (2007)

    Article MATH MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China

    Zhen Wang & Dachuan Xu

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

    Donglei Du

Authors
  1. Zhen Wang
  2. Donglei Du
  3. Dachuan Xu

Editor information

Editors and Affiliations

  1. Warwick Business School/ DIMAP - Centre for Discrete Mathematics and its Applications Coventry, University of Warwick, CV4 7AL, UK

    Bo Chen

Rights and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Z., Du, D., Xu, D. (2010). A Primal-Dual Approximation Algorithm for thek-Level Stochastic Facility Location Problem. In: Chen, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2010. Lecture Notes in Computer Science, vol 6124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14355-7_26

Download citation

Publish with us

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide -see info

Tax calculation will be finalised at checkout

Purchases are for personal use only


[8]ページ先頭

©2009-2025 Movatter.jp