Skip to main content

Online Bin Packing with (1,1) and (2,R) Bins

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8287))

  • 1197 Accesses

Abstract

We study a variant of online bin packing problem, in which there are two types of bins: (1,1) and (2,R), i.e., unit size bin with cost 1 and size 2 bin with cost R > 1, the objective is to minimize the total cost occurred when all the items are packed into the two types of bins. It is not difficult to see that the offline version of the problem is equivalent to the classical bin packing problem when R > 3. In this paper, we focus on the case R ≤ 3, and propose online algorithms and obtain lower bounds for the problem.

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

Access this chapter

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Epstein, L., Levin, A.: An APTAS for Generalized Cost Variable-Sized Bin Packing. SIAM J. Comput. 38(1), 411–428 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ullman, J.D.: The performance of a memory allocation algorithm. Technical Report 100, Princeton University, Princeton, NJ (1971)

    Google Scholar 

  3. Johnson, D.S.: Fast algorithm for bin packing. Journal of Computer and System Sciences 8, 272–314 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  4. Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3, 256–278 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  5. Yao, A.C.C.: New algorithms for bin packing. J. ACM 27, 207–227 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Coffman, E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin packing: A survey. In: Hochbaum, D. (ed.) Approximation Algorithms. PWS Publishing Company (1997)

    Google Scholar 

  7. Lee, C.C., Lee, D.T.: A simple on-line bin packing algorithm. J. ACM 32(3), 256–278 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  8. Van Vliet, A.: An improved lower bound for on-line bin packing algorithms. Information Processing Letters 43(5), 277–284 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Seiden, S.S.: On the online bin packing problem. J. ACM 49, 640–671 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Seiden, S.S., Van Stee, R., Epstein, L.: New bounds for variable-sized online bin packing. SIAM J. Comput. 32(2), 455–469 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Friesten, D.K., Langston, M.A.: Variable sized bin packing. SIAM J. Comput. 15, 222–230 (1986)

    Article  MATH  Google Scholar 

  12. Kinnerseley, N.G., Langston, M.A.: Online variable-sized bin packing. Discrete Applied Mathematics 22(2), 143–148 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  13. Csirik, J.: An on-line algorithm for variable-sized bin packing. Acta Informatica 26(8), 697–709 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. Brown, D.J.: A lower bound for on-line one-dimensional bin packing algorithms. Tech. report -864. Coordinated Science Laboratory Urbana IL (1979)

    Google Scholar 

  15. Liang, F.M.: A lower bound for on-line bin packing. Information Processing Letters 10, 76–79 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  16. Van Vliet, A.: An improved lower bound for online bin packing algorithm. Inform. Process. Lett. 43, 277–284 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  17. Van Vliet, A.: Lower and upper bounds for online bin packing and scheduling heuristics. Thesis Publishers, Amsterdam (1995)

    Google Scholar 

  18. Blitz, D., Van Vliet, A., Woeginger, G.J.: Lower bounds on the asymptotic worst-case ratio of online bin packing algorithms (1996) (unpublished manuscript)

    Google Scholar 

  19. Valerio de Carvalho, J.M.: LP models for bin packing and cutting stock problem. European Journal of Operational Research 141, 253–273 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Chen, J., Han, X., Iwama, K., Ting, HF. (2013). Online Bin Packing with (1,1) and (2,R) Bins. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03780-6_34

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03779-0

  • Online ISBN: 978-3-319-03780-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics