Skip to main content
Log in

Choosing the Capacity of Arcs with Constraint on Flow Delay Time

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The authors consider the problem of choosing the capacity of arcs from a given set, which is important in flow distribution in multicommodity communication networks with constraint on flow delay time. Such problem is proved to be NP-hard. The algorithms for the approximate solution of the problem and results of their experimental comparison with exact algorithm based on generating a sequence of binary reflected Gray codes are given. It is noted that obtaining an exact solution is possible with the use of pseudopolynomial algorithms for the 0–1 multiple-choice knapsack problem.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Kleinrock, Queueuing Systems, Vol. II, Computer Applications, John Wiley & Sons, New York (1976).

    MATH  Google Scholar 

  2. D. Bertsekas and R. Gallager, Data Networks, Prentice-Hall Inc., Englewood Cliffs (1992).

    MATH  Google Scholar 

  3. Yu. P. Zaichenko, “The problem of designing the structure of distributed computer networks,” Avtomatika, No. 4, 35–44 (1981).

  4. E. Yu. Zaichenko, “A complex of models and algorithms for optimization of characteristics of networks with MPLS technology,” Systemni Doslidzh. ta Inform. Tekhnologii, No. 4, 58–71 (2007).

  5. O. M. Trofymchuk and V. A. Vasyanin, “Simulation of packing, distribution and routing of small-size discrete flows in a multicommodity network,” J. of Autom. and Inform. Sci., Vol. 47, Iss. 7, 15–30 (2015).

  6. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman & Co., New York (1979).

    MATH  Google Scholar 

  7. R. M. Karp, “Reducibility among combinatorial problems,” in: R. E. Miller and J. W. Thatcher (eds.), Complexity of Computer Computations, Proc. Symp. on the Complexity of Computer Computations, IBM Thomas J. Watson Research Center, Plenum Press, Yorktown Heights, New York (1972), pp. 85–103.

  8. V. S. Mikhalevich and N. Z. Shor, “Numerical solutions of multiple-choice problems by the method of sequential analysis of variants,” Scientific and Methodical Materials of the Economic-Mathematical Seminar [in Russian], Issue 1, Rotaprint AN USSR, LEMI, Moscow (1962), pp. 15–42.

  9. V. S. Mikhalevich, “Sequential optimization algorithms and their application,” Pt. I, Cybernetics, Vol. 1, No. 1, 44–55 (1965); Pt. II Cybernetics, Vol. 1, No. 2, 87–92 (1965).

  10. V. L. Volkovich and A. F. Voloshin, “A scheme of the method of sequential analysis and sifting of variants,” Cybernetics, Vol. 14, No. 4, 585–593 (1978).

    Article  Google Scholar 

  11. V. S. Mikhalevich, V. L. Volkovich, A. F. Voloshin, and Yu. M. Pozdnyakov, “Algorithms for sequential analysis and fathoming in discrete optimization problems,” Cybernetics, Vol. 16, No. 3, 389–399 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Martelo and P. Toth, Knapsack Problems: Algorithms and Computer Implementations, Wiley, Chichester (1990).

    Google Scholar 

  13. H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems, Springer-Verlag, Berlin–Heidelberg (2004).

    Book  MATH  Google Scholar 

  14. M. S. Bansal and V. Ch. Venkaiah, “Improved fully polynomial time approximation scheme for the 0–1 multiple-choice knapsack problem,” Technical Report Number: IIIT-H/TR/2004/003, IIIT, Hyderabad, India (2004).

  15. B. Suri, U. D. Bordoloi, and P. Eles, “A scalable GPU-based approach to accelerate the multiple-choice knapsack problem,” in: Design, Automation & Test in Europe Conference & Exhibition (DATE), 12–16 March 2012, IEEE, Dresden (2012). https://doi.org/10.1109/DATE.2012.6176665.

  16. D. Rhee, Faster Fully Polynomial Approximation Schemes for Knapsack Problems, Massachusetts Institute of Technology Operations Research Center, Boston (2015). URL: http://hdl.handle.net/1721.1/98564.

  17. E. M. Bednarczuk, J. Miroforidis, and P. Pyzel, “A multi-criteria approach to approximate solution of multiple-choice knapsack problem,” Computational Optimization and Applications, Vol. 70, Iss. 3, 889–910 (2018).

  18. J. R. Bitner, G. Ehrlich, and E. M. Reingold, “Efficient generation of the binary reflected Gray code and its applications,” Comm. ACM, Vol. 19, Iss. 9, 517–521 (1976).

  19. D. E. Knuth, The Art of Computer Programming, Vol. 4A, Combinatorial Algorithms, Part 1, Addison Wesley Longman, Boston (2011).

  20. J. O. Cerdeira and P. Barcia, “When is a 0–1 knapsack a matroid?” Portugaliae Mathematica, No. 52, 475–480 (1995).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to O. M. Trofymchuk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2019, pp. 50–60.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Trofymchuk, O.M., Vasyanin, V.A. Choosing the Capacity of Arcs with Constraint on Flow Delay Time. Cybern Syst Anal 55, 561–569 (2019). https://doi.org/10.1007/s10559-019-00165-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-019-00165-0

Keywords

Navigation