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» The Arithmetical Complexity of Dimension and Randomness
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FOCS
1991
IEEE
14 years 3 days ago
A General Approach to Removing Degeneracies
We wish to increase the power of an arbitrary algorithm designed for non-degenerate input, by allowing it to execute on all inputs. We concentrate on in nitesimal symbolic perturba...
Ioannis Z. Emiris, John F. Canny
PDCAT
2005
Springer
14 years 2 months ago
Optimal Routing in a Small-World Network
Recently a bulk of research [14, 5, 15, 9] has been done on the modelling of the smallworld phenomenon, which has been shown to be pervasive in social and nature networks, and eng...
Jianyang Zeng, Wen-Jing Hsu
SAC
2006
ACM
14 years 2 months ago
The impact of sample reduction on PCA-based feature extraction for supervised learning
“The curse of dimensionality” is pertinent to many learning algorithms, and it denotes the drastic raise of computational complexity and classification error in high dimension...
Mykola Pechenizkiy, Seppo Puuronen, Alexey Tsymbal
ISSAC
2005
Springer
105views Mathematics» more  ISSAC 2005»
14 years 2 months ago
Computing the rank and a small nullspace basis of a polynomial matrix
We reduce the problem of computing the rank and a nullspace basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n×n matrix of degree d over ...
Arne Storjohann, Gilles Villard
FOCS
2004
IEEE
14 years 10 days ago
Hardness of Approximating the Shortest Vector Problem in Lattices
Let p > 1 be any fixed real. We show that assuming NP RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in p norm within a constant ...
Subhash Khot