Quantum and randomized lower bounds for local search on vertex-transitive graphs

@article{Dinh2008QuantumAR,
  title={Quantum and randomized lower bounds for local search on vertex-transitive graphs},
  author={Hang T. Dinh and Alexander Russell},
  journal={Quantum Information & Computation},
  year={2008},
  volume={10},
  pages={636-652}
}
We study the problem of local search on a graph. Given a real-valued black-box functionf on the graph's vertices, this is the problem of determining a local minimum of f--a vertex v for which f(v) is no more than f evaluated at any of v's neighbors. In1983, Aldous gave the first strong lower bounds for the problem, showing that anyrandomized algorithm requires Ω(2n/2-o(n)) queries to determine a local minimum onthe n-dimensional hypercube. The next major step forward was not until 2004… CONTINUE READING