Quantum Query Complexity of Some Graph Problems

  • Christoph Dürr
  • Mark Heiligman
  • Peter Høyer
  • Mehdi Mhalla
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)


Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Source Shortest Paths. For example we show that the query complexity of Minimum Spanning Tree is in Θ(n 3/2) in the matrix model and in \(\Theta(\sqrt{nm})\) in the array model, while the complexity of Connectivity is also in Θ(n 3/2) in the matrix model, but in Θ(n) in the array model. The upper bounds utilize search procedures for finding minima of functions under various conditions.


Span Tree Matrix Model Undirected Graph Quantum Algorithm Query Complexity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Christoph Dürr
    • 1
  • Mark Heiligman
    • 2
  • Peter Høyer
    • 3
  • Mehdi Mhalla
    • 4
  1. 1.Laboratoire de Recherche en Informatique, UMR 8623Université Paris-SudOrsayFrance
  2. 2.Advanced Research and Development Activity, Suite 6644National Security AgencyFort MeadeUSA
  3. 3.Dept. of Computer ScienceUniv. of CalgaryCanada
  4. 4.Laboratoire LeibnizInstitut IMAGGrenobleFrance

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