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» The lattice dimension of a graph
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83
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ISSAC
2007
Springer
105views Mathematics» more  ISSAC 2007»
15 years 6 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
113
Voted
FOCS
2004
IEEE
15 years 4 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
97
Voted
EUROGRAPHICS
2010
Eurographics
15 years 9 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»
15 years 23 days 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»
14 years 10 days 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