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CVPR
2012
IEEE
9 years 3 months ago
See all by looking at a few: Sparse modeling for finding representative objects
We consider the problem of finding a few representatives for a dataset, i.e., a subset of data points that efficiently describes the entire dataset. We assume that each data poi...
Ehsan Elhamifar, Guillermo Sapiro, René Vid...
SODA
2012
ACM
217views Algorithms» more  SODA 2012»
9 years 3 months ago
Deterministic construction of an approximate M-ellipsoid and its applications to derandomizing lattice algorithms
We give a deterministic O(log n)n -time and space algorithm for the Shortest Vector Problem (SVP) of a lattice under any norm, improving on the previous best deterministic nO(n) -...
Daniel Dadush, Santosh Vempala
CORR
2010
Springer
178views Education» more  CORR 2010»
11 years 2 days ago
Enumerative Algorithms for the Shortest and Closest Lattice Vector Problems in Any Norm via M-Ellipsoid Coverings
We give an algorithm for solving the exact Shortest Vector Problem in n-dimensional lattices, in any norm, in deterministic 2O(n) time (and space), given poly(n)-sized advice that...
Daniel Dadush, Chris Peikert, Santosh Vempala
FOCS
2004
IEEE
11 years 5 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
STACS
2004
Springer
11 years 6 months ago
Lattices with Many Cycles Are Dense
Abstract We give a method for approximating any n-dimensional lattice with a lattice Λ whose factor group Zn /Λ has n − 1 cycles of equal length with arbitrary precision. We al...
Mårten Trolin
STOC
2006
ACM
141views Algorithms» more  STOC 2006»
12 years 1 months ago
Lattice problems and norm embeddings
We present reductions from lattice problems in the 2 norm to the corresponding problems in other norms such as 1, (and in fact in any other p norm where 1 p ). We consider latt...
Oded Regev, Ricky Rosen
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