A Bounded Item Bin Packing Problem over Discrete Distribution

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3959))

  • 1071 Accesses

Abstract

In this paper we formulate a bounded item bin packing problem over discrete distribution (BIBPPOD) in computer and communication networks, and consider the average performance ratio for next fit algorithm. An efficient average-case analysis procedure for finding the average performance ratio and problem solution is demonstrated. We give the closed-form expression for some special range to which the bounded item belongs. Our result is useful for designing the length in fixed-size format or evaluating the performance impacted by the protocol header in computer and communication network.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 85.59
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 106.99
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** 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.

Similar content being viewed by others

References

  1. Coffman, E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin packing: A survey. In: Hochbaum, D. (ed.) Approximation Algorithms for NP-Hard Problems, pp. 46–93. PSW publishing, Boston (1996)

    Google Scholar 

  2. Laguna, M., Glover, F.: Bandwidth packing: A tabu search approach. Management Science 39, 492–500 (1993)

    Article  MATH  Google Scholar 

  3. Park, K., Kang, S., Park, S.: An integer programming approach to the bandwidth packing problem. Management Science 42, 1277–1291 (1996)

    Article  MATH  Google Scholar 

  4. Parker, M., Ryan, J.: A column generation algorithm for bandwidth packing. Telecommunication Systems 2, 185–196 (1995)

    Article  Google Scholar 

  5. Ali, A., Barkhi, R.: The Multi-Hour Bandwidth Packing Problem. Computers and OR 27, 1–14 (2000)

    Article  MATH  Google Scholar 

  6. Coffman Jr., E.G., Feldmann, A., Kahale, N., Poonen, B.: Computing Call Admission Capacities in Linear Networks. Prob. Eng. Inf. Sci., 387–406 (1999)

    Google Scholar 

  7. Coffman Jr., E.G., Stolyar, A.L.: Bandwidth Packing. Algorithmica 29, 70–88 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Zimmermann, H.: OSI Reference Model - The ISO Model of Architecture for Open Systems Interconnection. IEEE Transactions on Communication 28(4), 425–432 (1980)

    Article  Google Scholar 

  9. Comer, D.: Internetworking with TCP/IP. Prentice Hall, Englewood Cliffs (1988)

    Google Scholar 

  10. Why Modern Switch Fabrics use a Fixed-Size Frame Format, whitepaper (2005)

    Google Scholar 

  11. Jr. Coffman, E., So, K., Hofri, M., Yao, A.: A stochasitic model of Bin-Packing. Information and Control 44, 105–115 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  12. Karmarkar, N.: Probability analysis of some bin packing algorithms. In: Proceedings of the 23rd Annual symposium on foundations of Computer Science, pp. 107–111 (1982)

    Google Scholar 

  13. Tsuga, K.: Average-case Analysis of On-line Bin Packing Algorithms, Masters Thesis, Dept. of Computer-Scienece, Univ. of California, Santa Barbara, CA (1986)

    Google Scholar 

  14. Coffman Jr., E.G., Halfin, S., Jean-Marie, A., Robert, P.: Stochastic analysis of a slotted FIFO communication channel. IEEE Trans. on Info. Theory 39(5), 1555–1566 (1993)

    Article  MATH  Google Scholar 

  15. Menakerman, N., Rom, R.: Analysis of Transmissions Scheduling with Packet Fragmentation. Discrete Mathematics and Theoretical Computer Science 4, 139–156 (2001)

    MATH  MathSciNet  Google Scholar 

  16. Coffman Jr., E.G., Courcoubetis, C., Garey, M.R., Johnson, D.S., Shor, P.W., Weber, R.R., Yannakakis, M.: Bin Packing with Discrete Item Sizes, Part I: Perfect Packing Theorems and the Average Case Behavior of Optimal Packings. SIAM J. Discrete Mathematics 13, 384–402 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Rhee, T., Talagrand, M.: Martingale inequalities and NP-complete problems. Mathematical Operations Research 12, 177–181 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  18. Coffman Jr., E.G., Lueker, G.S.: Probabilistic Analysis of Packing and Partitioning Algorithms. Wiley, New York (1991)

    Google Scholar 

  19. Menakerman, N., Rom, R.: Average Case Analysis of Bounded Space Bin Packing Algorithms, EE Publication No.1274 (2000)

    Google Scholar 

  20. Brualdi, R.A.: Introductory combinatorics, 3rd edn., pp. 205–208. Prentice Hall, Englewood Cliffs (1999)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, J., Yang, Y., Zhu, H., Zeng, P. (2006). A Bounded Item Bin Packing Problem over Discrete Distribution. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_10

Download citation

  • DOI: https://doi.org/10.1007/11750321_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34021-8

  • Online ISBN: 978-3-540-34022-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Navigation