Quantum Query Complexity of Some Graph Problems

@article{Drr2006QuantumQC,
  title={Quantum Query Complexity of Some Graph Problems},
  author={C. D{\"u}rr and M. Heiligman and P. H{\o}yer and M. Mhalla},
  journal={SIAM J. Comput.},
  year={2006},
  volume={35},
  pages={1310-1328}
}
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 $\Theta(n^{3/2})$ in the matrix model and in $\Theta(\sqrt{nm})$ in the array model, while the… Expand
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