On the bipartite unique perfect matching problem

Authors:
Thanh Minh Hoang;Meena Mahajan;Thomas Thierauf
Affiliations:
Abt. Theor. Inform., Universität Ulm, Ulm, Germany;Inst. of Math. Sciences, Chennai, India;Fak. Elektr. und Inform., Aalen University, Aalen, Germany
Venue:
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Year:
2006

Citing 13
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Abstract

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 NC2. 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.