Quantum Algorithms for Matching and Network Flows

  • Andris Ambainis
  • Robert Špalek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3884)


We present quantum algorithms for some graph problems: finding a maximal bipartite matching in time \(O(n\sqrt{m}logn)\), finding a maximal non-bipartite matching in time \(O(n^2(\sqrt{m/n}+log n)log n)\), and finding a maximal flow in an integer network in time \(O(min(n^{7/6} \sqrt{m} \cdot U^{1/3},\sqrt{nU}m)log n)\), where n is the number of vertices, m is the number of edges, and Un 1/4 is an upper bound on the capacity of an edge.


Network Flow Quantum Algorithm Classical Algorithm Graph Problem Bipartite Match 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Robert Špalek
    • 2
  1. 1.Institute for Quantum Computing and University of WaterlooCanada
  2. 2.CWI and University of AmsterdamThe Netherlands

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