Skip to main content
SpringerLink
Log in

A Cost-Sharing Scheme for the k-Product Facility Location Game with Penalties

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14423))

Included in the following conference series:

  • 286 Accesses

Abstract

In the k-product facility location game with penalties, each customer must be supplied with k different products or be rejected by paying the penalty cost. The game is considered in this paper. The cost-sharing scheme for this game refers to allocating the costs of the problem to all customers. We present a cross-monotonic and competitive scheme which satisfies 2 and \((\frac{3k}{2}-\frac{3}{2})\)-approximate cost recovery when \(k=2\) and \(k \ge 3\), respectively. Moreover, the lower bound of the cost-sharing scheme is obtained for the k-product facility location game with penalties.

This research was supported by the National Natural Science Foundation of China under Grant 11871213.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

References

  1. Aardal, K., Chudak, F.A., Shmoys, D.B.: A 3-approximation algorithm for the \(k\)-level uncapacitated facility location problem. Inf. Process. Lett. 72, 161–167 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. An, H.C., Singh, M., Svensson, O.: LP-based algorithms for capacitated facility location. SIAM J. Comput. 46, 272–306 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristic for \(k\)-median and facility location problems. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pp. 21–29 (2001)

    Google Scholar 

  4. Charikar, M., Khuller, S., Mount, D.M., et al.: Algorithms for facility location problems with outliers. In: Proceedings of the Twelfth Annual Symposium on Discrete Algorithm, pp. 642–651 (2001)

    Google Scholar 

  5. Chen, X., Fang, Q., Liu, W., Ding, Y., Nong, Q.: Strategyproof mechanisms for 2-facility location games with minimax envy. J. Comb. Optim. 43, 1628–1644 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, Z., Fong, K.C., Li, M., Wang, K., Yuan, H., Zhang, Y.: Facility location games with optional preference. Theor. Comput. Sci. 847, 185–197 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cheng, Y., Yu, W., Zhang, G.: Strategy-proof approximation mechanisms for an obnoxious facility game on networks. Theor. Comput. Sci. 497, 154–163 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chudak, F.A., Shmoys, D.B.: Improved approximation algorithms for the uncapacitated facility location problem. SIAM J. Comput. 33, 1–25 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Huang, H.C., Li, R.: A \(k\)-product uncapacitated facility location problem. Eur. J. Oper. Res. 185, 552–562 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Immorlica, N., Mahdian, M., Mirrokni, V.S.: Limitations of cross-monotonic cost-sharing schemes. ACM Trans. Algor. 4, 1–25 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, M., Wang, C., Zhang, M.: Budgeted facility location games with strategic facilities. In: Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence, pp. 400–406 (2021)

    Google Scholar 

  14. Moulin, H., Shenker, S.: Strategyproof sharing of submodular costs: budget balance versus efficiency. Econ. Theory. 18, 511–533 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pál, M., Tardos, É.: Group strategy proof mechanisms via primal-dual algorithms. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 584–593 (2003)

    Google Scholar 

  16. Shmoys, D.B., Tardos, É., Aardal, K.: Approximation algorithms for facility location problems. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 265–274 (1997)

    Google Scholar 

  17. Wang, F.M., Wang, J.J., Li, N., Jiang, Y.J., Li, S.C.: A cost-sharing scheme for the \(k\)-level facility location game with penalties. J. Oper. Res. Soc. China. 10, 173–182 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, Z., Xu, D.: A cost-sharing method for an uncapacitated facility location game with penalties. J. Syst. Sci. Complex. 25, 287–292 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Xu, D., Du, D.: The \(k\)-level facility location game. Oper. Res. Lett. 34, 421–426 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ye, D., Mei, L., Zhang, Y.: Strategy-proof mechanism for obnoxious facility location on a line. In: Proceedings of the 21st International Conference on Computing and Combinatorics, pp. 45–56 (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Xiaowei Li & Xiwen Lu

Authors
  1. Xiaowei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiwen Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiwen Lu .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. University of Delaware, Newark, DE, USA

    Guangmo Tong

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Li, X., Lu, X. (2024). A Cost-Sharing Scheme for the k-Product Facility Location Game with Penalties. In: Wu, W., Tong, G. (eds) Computing and Combinatorics. COCOON 2023. Lecture Notes in Computer Science, vol 14423. Springer, Cham. https://doi.org/10.1007/978-3-031-49193-1_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-49193-1_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49192-4

  • Online ISBN: 978-3-031-49193-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation