On the Bipartite Unique Perfect Matching Problem

  • Thanh Minh Hoang
  • Meena Mahajan
  • Thomas Thierauf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


In this note, we give tighter bounds on the complexity of the bipartite unique perfect matching problem, bipartite-UPM. We show that the problem is in C = L and in NL  ⊕ L, both subclasses of NC 2.

We also consider the (unary) weighted version of the problem. We show that testing uniqueness of the minimum-weight perfect matching problem for bipartite graphs is in \({\rm \bf L}^{{\rm \bf C_=L}}\) and in NL  ⊕ L.

Furthermore, we show that bipartite-UPM is hard for NL.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thanh Minh Hoang
    • 1
  • Meena Mahajan
    • 2
  • Thomas Thierauf
    • 3
  1. 1.Abt. Theor. Inform.Universität UlmUlmGermany
  2. 2.Inst. of Math. SciencesChennaiIndia
  3. 3.Fak. Elektr. und Inform.Aalen UniversityAalenGermany

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