Journal of Mathematical Sciences

, Volume 181, Issue 6, pp 782–791 | Cite as

Minimum—weight perfect matching for nonintrinsic distances on the line


We consider a minimum-weight perfect matching problem on the line and establish a “bottom-up” recursion relation for weights of partial minimum-weight matchings. Bibliography: 11 titles.


Perfect Match Recursion Relation Match Problem Perfect Match Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Aggarwal, A. Bar-Noy, S. Khuller, D. Kravets, and B. Schieber, “Efficient minimum cost matching using quadrangle inequality,” J. Algorithms, 19, No. 1, 116-143 (1995).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, Amer. Math. Soc., Providence, Rhode Island (2001).MATHGoogle Scholar
  3. 3.
    W. Cook and A. Rohe, “Computing minimum-weight perfect matching,” INFORMS J. Comput., 11, No. 2, 138-148 (1999).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    J. Delon, J. Salomon, and A. Sobolevski, “Local matching indicators for concave transport costs,” C. R. Acad. Sci. Paris Sér. I Math., 348, No. 15-16, 901-905 (2010).MATHCrossRefGoogle Scholar
  5. 5.
    J. Delon, J. Salomon, and A. Sobolevski, “Local matching indicators for transport problems with concave costs,” in preparation.Google Scholar
  6. 6.
    J. Edmonds, “Maximum matching and a polyhedron with 0,1-vertices,” J. Res. Nat. Bur. Standards, 6913, 125-130 (1965).MathSciNetGoogle Scholar
  7. 7.
    J. Edmonds, “Paths, trees and flowers,” Canad. J. Math., 17, 449-467 (1965).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    J. Heinonen, Lectures on Analysis in Metric Spaces, Springer-Verlag, New York (2061).Google Scholar
  9. 9.
    R. M. Karp and S. Y. R. Li, “Two special cases of the assignment prob1em,” Discrete Math., 13, 129-142 (1975).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    R. J. McCann, “Exact solutions to the transportation problem on the line,” Prac. R. Sac. Lond. Ser. A Math. Phys. Eng. Sci., 455, 1341-1386 (1989).MathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Werman, S. Peleg, R. Melter and T. Y. Kong, “Bipartite graph matching for points on a line or a circle,” J. Algorithms, 7, No. 2, 277-284 (1986).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.LTCI CNRS TELECOM ParisTechParisFrance
  2. 2.CEREMADE, Université Paris-DauphineParisFrance
  3. 3.Insnitute for Information Transmission Problems (Kharkevich Institute)MoscowRussia
  4. 4.Laboratoire J.-V. Poncelet (UMI 2615 CNRS)MoscowRussia
  5. 5.Moscow Institute for Physics and Technology (MIPT)MoscowRussia

Personalised recommendations