Skip to main content
Log in

Optimal sharing

  • Published:
Mathematical Programming Submit manuscript

Abstract

We investigate a sharing method to distribute a given quantity of resources equitably through a capacity-constrained distribution network. The sharing, called an optimal sharing, not only maximizes the minimum share but also minimizes the maximum share. The optimal sharing is obtained in time O(|T| c(n e)) where |T| is the number of sinks in the network andc(n, e) is the time required to solve the maximum flow 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.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.R. Brown, “The sharing problem”,Operations Research 27 (1979) 324–340.

    Google Scholar 

  2. N. Christofides,Graph theory: an algorithmic approach (Academic Press, New York, NY, 1975).

    Google Scholar 

  3. S. Fujishige, “Lexicographically optimal base of polymatroid with respect to a weight vector”,Mathematics of Operations Research 5 (1980) 186–196.

    Google Scholar 

  4. Z. Galil and A. Naamad, “Network flows and generalized path compression”,Proceedings of ACM Symposia on the Theory of Computing 11 (1979) 13–26.

    Google Scholar 

  5. T. Ichimori, H. Ishii and T. Nishida, “A minimax flow problem”,Mathematica Japonica 24 (1979) 65–71.

    Google Scholar 

  6. T. Ichimori, H. Ishii and T. Nishida, “Finding the weighted minimax flow in polynomial time”,Journal of the Operations Research Society of Japan 23 (1980) 268–272.

    Google Scholar 

  7. M. Iri, “A review of recent work in Japan on principal partitions of matroids and their applications”,Annals of the New York Academy of Sciences 319 (1979) 306–319.

    Google Scholar 

  8. A.V. Karzanov, “Determining the maximum flow in a network by the method of preflows”,Soviet Mathematics Doklady 15 (1974) 434–437.

    Google Scholar 

  9. E.L. Lawler,Combinatorial optimization: networks and matroids (Holt, Rinehart and Winston, New York, NY 1976).

    Google Scholar 

  10. N. Megiddo, “Optimal flows in networks with multiple sources and sinks”,Mathematical Programming 7 (1974) 97–107.

    Google Scholar 

  11. M. Megiddo, “A good algorithm for lexicographically optimal flows in multi-terminal networks”,Bulletin of the American Mathematical Society 83 (1977) 407–409.

    Google Scholar 

  12. D.F. Stanat and G.A. Magó, “Minimizing maximum flows in linear graphs”,Networks 9 (1979) 333–361.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ichimori, T., Ishii, H. & Nishida, T. Optimal sharing. Mathematical Programming 23, 341–348 (1982). https://doi.org/10.1007/BF01583798

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01583798

Key words

Navigation