Quantum algorithms for the triangle problem

@inproceedings{Magniez2005QuantumAF,
  title={Quantum algorithms for the triangle problem},
  author={F. Magniez and M. Santha and M. Szegedy},
  booktitle={SODA '05},
  year={2005}
}
We present two new quantum algorithms that either find a triangle (a copy of <i>K</i><inf>3</inf>) in an undirected graph <i>G</i> on <i>n</i> nodes, or reject if <i>G</i> is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes <i>Õ</i>(<i>n</i><sup>10/7</sup>) queries. The second algorithm uses <i>Õ</i>(<i>n</i><sup>13/10</sup>) queries, and it is based on a new design concept of Ambainis [6] that incorporates the benefits of quantum walks into Grover search… Expand
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