Skip to main content
SpringerLink
Log in

An Incentive Mechanism for Selfish Bin Covering

  • Conference paper
  • First Online:
Combinatorial Optimization and Applications (COCOA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10043))

Abstract

In this paper, we consider the selfish bin covering problems, which can be viewed as the bin covering problems in game theoretic settings. Our main contribution is an incentive mechanism with better price of anarchy. Under this mechanism, for any instance with a Nash equilibrium (NE), we show that price of anarchy is 2/3. For the cases that the NE does not exist, we propose a concept of modified NE, named M-NE, which can be obtained in finite steps from any initial state. We further show that for M-NE, the price of anarchy is 1/2 and the price of stability is 1.

The work is partially supported by National Natural Science Foundation of China (NSFC) (NO. 11271341 and 11501316).

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Notes

  1. 1.

    The PoA of selfish bin packing is defined contrary to that of SBC.

  2. 2.

    First Fit Decreasing, which is described as follows. First sort the items in non-increasing order of their sizes, then puts the items one by one in this order to a bin until the bin is covered. Open a new bin and repeat the above actions until all the items are assigned.

References

  1. Adar, R., Epstein, L.: Selfish bin packing with cardinality constraints. Theoret. Comput. Sci. 495, 66–80 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Assmann, S.B.: Problems in discrete applied mathematics. Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA (1983)

    Google Scholar 

  3. Assmann, S.F., Johnson, D.S., Kleitman, D.J., Leung, J.Y.-T.: On a dual version of the one-dimensional bin packing problem. J. Algorithms 5(4), 502–525 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bilò, V.: On the packing of selfish items. In: Proceedings 20th IEEE International Parallel & Distributed Processing Symposium, p. 9. IEEE (2006)

    Google Scholar 

  5. Cao, Z., Yang, X.: Selfish bin covering. Theoret. Comput. Sci. 412(50), 7049–7058 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Csirik, J., Frenk, J.B.G., Labbé, M., Zhang, S.: Two simple algorithms for bin covering. Acta Cybernetica 14(1), 13–25 (1999)

    MathSciNet  MATH  Google Scholar 

  7. Csirik, J., Johnson, D.S., Kenyon, C.: Better approximation algorithms for bin covering. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 557–566. Society for Industrial and Applied Mathematics (2001)

    Google Scholar 

  8. Coffman, E.G., Csirik, J., Leung, J.Y.-T.: Variants of classical one-dimensional bin packing. In: Handbook of Approximation Algorithms and Metaheuristics, p. 13 (2007). Chap. 33

    Google Scholar 

  9. Dósa, G., Epstein, L.: Generalized selfish bin packing. arXiv preprint arXiv:1202.4080 (2012)

  10. Epstein, L., Kleiman, E.: Selfish bin packing. Algorithmica 60(2), 368–394 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jansen, K., Solis-Oba, R.: An asymptotic fully polynomial time approximation scheme for bin covering. Theoret. Comput. Sci. 306(1), 543–551 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Ma, R., Dósa, G., Han, X., Ting, H.-F., Ye, D., Zhang, Y.: A note on a selfish bin packing problem. J. Global Optim. 56(4), 1457–1462 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Papadimitriou, C.: Algorithms, games, and the internet. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, 749–753. ACM (2001)

    Google Scholar 

  15. Yu, G., Zhang, G.: Bin packing of selfish items. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 446–453. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, China

    Weian Li, Qizhi Fang & Wenjing Liu

Authors
  1. Weian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qizhi Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenjing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenjing Liu .

Editor information

Editors and Affiliations

  1. University of Hong Kong, Hong Kong, China

    T-H. Hubert Chan

  2. City University of Hong Kong, Hong Kong, China

    Minming Li

  3. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Li, W., Fang, Q., Liu, W. (2016). An Incentive Mechanism for Selfish Bin Covering. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_46

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48749-6_46

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48748-9

  • Online ISBN: 978-3-319-48749-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation