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» On the Homological Dimension of Lattices
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DCC
2006
IEEE
14 years 6 months ago
Optimal Index Assignment for Multiple Description Lattice Vector Quantization
Optimal index assignment of multiple description lattice vector quantizer (MDLVQ) can be posed as a large-scale linear assignment problem. But is this expensive algorithmic approa...
Xiang Huang, Xiaolin Wu
ISSAC
2007
Springer
105views Mathematics» more  ISSAC 2007»
14 years 26 days 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
13 years 10 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
14 years 3 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»
13 years 6 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. ...