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» Quantum query complexity of minor-closed graph properties
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FOCS
2003
IEEE
15 years 6 months ago
Quantum Search of Spatial Regions
: Can Grover’s algorithm speed up search of a physical region—for example a 2-D grid of size √ n × √ n? The problem is that √ n time seems to be needed for each query, j...
Scott Aaronson, Andris Ambainis
121
Voted
STOC
2006
ACM
166views Algorithms» more  STOC 2006»
16 years 1 months ago
New upper and lower bounds for randomized and quantum local search
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexi...
Shengyu Zhang
118
Voted
STOC
2004
ACM
153views Algorithms» more  STOC 2004»
16 years 1 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 phr...
Miklos Santha, Mario Szegedy
APPROX
2008
Springer
89views Algorithms» more  APPROX 2008»
15 years 2 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 v...
Hang Dinh, Alexander Russell
FOCS
2006
IEEE
15 years 6 months ago
On the Quantum Query Complexity of Local Search in Two and Three Dimensions
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been...
Xiaoming Sun, Andrew Chi-Chih Yao