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ISSAC
2007
Springer
105views Mathematics» more  ISSAC 2007»
15 years 3 months ago
Certification of the QR factor R and of lattice basis reducedness
Given a lattice basis of n vectors in Zn, we propose an algorithm using 12n3 + O(n2) floating point operations for checking whether the basis is LLL-reduced. If the basis is redu...
Gilles Villard
FOCS
2004
IEEE
15 years 1 months 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
EUROGRAPHICS
2010
Eurographics
15 years 6 months ago
Fast High-Dimensional Filtering Using the Permutohedral Lattice
Many useful algorithms for processing images and geometry fall under the general framework of high-dimensional Gaussian filtering. This family of algorithms includes bilateral ...
Andrew Adams, Jongmin Baek, Myers Abraham Davis
DM
2008
103views more  DM 2008»
14 years 9 months ago
A note on lattice chains and Delannoy numbers
Fix nonnegative integers n1, . . . , nd and let L denote the lattice of integer points (a1, . . . , ad) Zd satisfying 0 ai ni for 1 i d. Let L be partially ordered by the usua...
John S. Caughman IV, Clifford R. Haithcock, J. J. ...
IACR
2011
141views more  IACR 2011»
13 years 9 months ago
Approximate common divisors via lattices
We analyze the multivariate generalization of Howgrave-Graham’s algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common...
Henry Cohn, Nadia Heninger