On optimal matchings


Givenn random red points on the unit square, the transportation cost between them is tipically √n logn.

This is a preview of subscription content, access via your institution.


  1. [1]

    L. R. Ford, Jr. andD. R. Fulkerson, A simple algorithm for finding maximal network flows and an application to the Hitchcock problem.Canad. J. Math. 9 (1957), 210–218.

    MATH  MathSciNet  Google Scholar 

  2. [2]

    R. Karp, Private communication (1982).

  3. [3]

    J. Komlós, P. Major andG. Tusnády, An approximation of partial sums of independent RV’s, and the sample DF.I. Z. Wahrscheinlichkeitstheorie verw. Gebiete 32 (1975), 111–131.

    MATH  Article  Google Scholar 

  4. [4]

    G. Schay, Nearest random variables with given distributions.Ann. of Probab. 2 (1974), 163–166.

    MATH  MathSciNet  Google Scholar 

  5. [5]

    G. Tusnády, A remark on the approximation of the sample DF in the multidimensional case.Periodica Mathematica Hungarica 8 (1977), 53–55.

    MATH  Article  MathSciNet  Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ajtai, M., Komlós, J. & Tusnády, G. On optimal matchings. Combinatorica 4, 259–264 (1984). https://doi.org/10.1007/BF02579135

Download citation

AMS subject classification (1980)

  • 60 D 05
  • 60 G 40