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» Quantum query complexity of minor-closed graph properties
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FOCS
2003
IEEE
14 years 4 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
STOC
2006
ACM
166views Algorithms» more  STOC 2006»
14 years 11 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
STOC
2004
ACM
153views Algorithms» more  STOC 2004»
14 years 11 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»
14 years 26 days 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
14 years 4 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