On Stable Matchings and Flows

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)


We describe a flow model that generalizes ordinary network flows the same way as stable matchings generalize the bipartite matching problem. We prove that there always exists a stable flow and generalize the lattice structure of stable marriages to stable flows. Our main tool is a straightforward reduction of the stable flow problem to stable allocations.


Stable marriages stable allocations network flows 


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  1. 1.
    Baïou, M., Balinski, M.: The stable allocation (or ordinal transportation) problem. Math. Oper. Res. 27(3), 485–503 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cechlárová, K., Fleiner, T.: On a generalization of the stable roommates problem. ACM Trans. Algorithms 1(1), 143–156 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dean, B.C., Munshi, S.: Faster algorithms for stable allocation problems. In: Proceedings of the MATCH-UP (Matching Under Preferences) Workshop at ICALP 2008, Reykjavik, pp. 133–144 (2008)Google Scholar
  4. 4.
    Fleiner, T.: A fixed point approach to stable matchings and some applications. Mathematics of Operations Research 28(1), 103–126 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fleiner, T.: On stable matchings and flows. Technical Report TR-2009-11, Egerváry Research Group, Budapest (2009),
  6. 6.
    Gale, D., Shapley, L.S.: College admissions and stability of marriage. Amer. Math. Monthly 69(1), 9–15 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Knuth, D.E.: Stable marriage and its relation to other combinatorial problems. American Mathematical Society, Providence (1997); An introduction to the mathematical analysis of algorithms, Translated from the French by Martin Goldstein and revised by the authorGoogle Scholar
  8. 8.
    Ostrovsky, M.: Stability in supply chain networks. American Economic Review 98(3), 897–923 (2006)CrossRefGoogle Scholar
  9. 9.
    Roth, A.E.: On the allocation of residents to rural hospitals: a general property of two-sided matching markets. Econometrica 54(2), 425–427 (1986)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Roth, A.E., Oliveria Sotomayor, M.A.: Two-sided matching. Cambridge University Press, Cambridge (1990); A study in game-theoretic modeling and analysis, With a foreword by Robert AumannCrossRefGoogle Scholar
  11. 11.
    Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific J. of Math. 5, 285–310 (1955)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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