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2004
ACM

Quantum and classical query complexities of local search are polynomially related

11 years 4 months ago
Quantum and classical query complexities of local search are polynomially related
Let f be an integer valued function on a finite set V . We call an undirected graph G(V, E) a neighborhood structure for f. The problem of finding a local minimum for f can be phrased as: for a fixed neighborhood structure G(V, E) find a vertex x V such that f(x) is not bigger than any value that f takes on some neighbor of x. The complexity of the algorithm is measured by the number of questions of the form "what is the value of f on x?" We show that the deterministic, randomized and quantum query complexities of the problem are polynomially related. This generalizes earlier results of Aldous [?] and Aaronson [?] and solves the main open problem in [?].
Miklos Santha, Mario Szegedy
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2004
Where STOC
Authors Miklos Santha, Mario Szegedy
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