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APPROX
2008
Springer

Quantum and Randomized Lower Bounds for Local Search on Vertex-Transitive Graphs

10 years 3 months ago
Quantum and Randomized Lower Bounds for Local Search on Vertex-Transitive Graphs
We study the problem of local search on a graph. Given a real-valued black-box function f 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. In 1983, Aldous gave the first strong lower bounds for the problem, showing that any randomized algorithm requires (2n/2-o(1) ) queries to determine a local minima on the n-dimensional hypercube. The next major step forward was not until 2004 when Aaronson, introducing a new method for query complexity bounds, both strengthened this lower bound to (2n/2 /n2 ) and gave an analogous lower bound on the quantum query complexity. While these bounds are very strong, they are known only for narrow families of graphs (hypercubes and grids). We show how to generalize Aaronson's techniques in order to give randomized (and quantum) lower bounds on the query complexity of local search for the family of vertex-transitive graphs. In parti...
Hang Dinh, Alexander Russell
Added 12 Oct 2010
Updated 12 Oct 2010
Type Conference
Year 2008
Where APPROX
Authors Hang Dinh, Alexander Russell
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