Combinatorica

, Volume 5, Issue 3, pp 247–255 | Cite as

A strongly polynomial minimum cost circulation algorithm

  • Éva Tardos
Article

Abstract

A new algorithm is presented for the minimum cost circulation problem. The algorithm is strongly polynomial, that is, the number of arithmetic operations is polynomial in the number of nodes, and is independent of both costs and capacities.

AMS subject classification (1980)

68 E 10 68 C 25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. P. Anstee, A polynomial algorithm forb-matching: an alternative approach,Research Report CORR 83–22, University Waterloo, Waterloo, Ontario, 1983.Google Scholar
  2. [2]
    W. H. Cunningham andA. Frank, A primal dual algorithm for submodular flows;Mathematics of Operations Research,10 (1985), 251–262.MATHMathSciNetGoogle Scholar
  3. [3]
    E. A. Dinits, Algorithm for solution of a problem of maximum flow in a network with power estimation;Soviet Math. Dokl.,11 (1970), 1277–1280.MATHGoogle Scholar
  4. [4]
    J. Edmonds, Systems of distinct representatives and linear algebra;J. Res. Nat. Bur. Standards,71 B (1967), 241–245.MathSciNetGoogle Scholar
  5. [5]
    J. Edmonds, Submodular functions, matroids and certain polyhedra, in:Combinatorial Structures and Applications, (R. K. Guy et al. eds.) 1970 Gordon and Breach, New York 67–87.Google Scholar
  6. [6]
    J. Edmonds andR. Giles, A min-max relation for submodular functions on graphs,Annals of Discrete Math. 1 (1977), 185–204.MathSciNetCrossRefGoogle Scholar
  7. [7]
    J. Edmonds andR. M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems,J. ACM 19 (1972), 248–264.MATHCrossRefGoogle Scholar
  8. [8]
    L. R. Ford, jr. andD. R. Fulkerson,Flows in Networks, Princeton University Press, Princeton N. J., 1962.MATHGoogle Scholar
  9. [9]
    D. R. Fulkerson, An Out-of-Kilter method for minimal cost flow problems,J. Soc. Indust. Appl. Math. 9 (1961), 18–27.MATHCrossRefGoogle Scholar
  10. [10]
    A. K. Lenstra, H. W. Lenstra, jr. andL. Lovász, Factoring polynomials with rational coefficients,Math. Ann. 261 (1982), 515–534.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    C. L. Lucchesi andD. H. Younger, A minimax theorem for directed graphs,J. London Math. Soc. 17 (1978), 368–374.CrossRefMathSciNetGoogle Scholar
  12. [12]
    N. Megiddo, Towards a genuinely polynomial algorithm for linear programming,SIAM J. Comput. 12 (1981), 347–353.CrossRefMathSciNetGoogle Scholar
  13. [13]
    G. J. Minty, Monotone Networks,Proc. Roy. Soc. London, Ser. A,257 (1960), 194–212.MATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    H. Röck, Scaling techniques for minimal cost network flows, in:Discrete Structures and Algorithms, (U. Page ed.) 1980, Carl Hanser, München, 181–191.Google Scholar

Copyright information

© Akadémiai Kiadó 1985

Authors and Affiliations

  • Éva Tardos
    • 1
  1. 1.Research Institute for TelecommunicationBudapestHungary

Personalised recommendations