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ICDT '99 Proceedings of the 7th International Conference on Database Theory
Approximation Algorithms for the Label-CoverMAX and Red-Blue Set Cover Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Approximability of Dense Instances of NEAREST CODEWORD Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
A Lattice-Based Public-Key Cryptosystem
SAC '98 Proceedings of the Selected Areas in Cryptography
Approximating Bounded Degree Instances of NP-Hard Problems
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Approximating SVPinfty to within Almost-Polynomial Factors Is NP-Hard
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Constraint Satisfaction: The Approximability of Minimization Problems
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Learning Halfspaces with Malicious Noise
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Learning Halfspaces with Malicious Noise
The Journal of Machine Learning Research
A new transference theorem in the geometry of numbers
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
On routing in circulant graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
A note on the subadditive network design problem
Operations Research Letters
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We prove the following about the Nearest Lattice Vector Problem (in any l/sub p/ norm), the Nearest Code-word Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NP-hard. 2. If for some /spl epsiv/0 there exists a polynomial time algorithm that approximates the optimum within a factor of 2/sup log(0.5-/spl epsiv/)/ /sup n/ then NP is in quasi-polynomial deterministic time: NP/spl sube/DTIME(n/sup poly(log/ /sup n)/). Moreover, we show that result 2 also holds for the Shortest Lattice Vector Problem in the l/sub /spl infin// norm. Improving the factor 2/sup log(0.5-/spl epsiv/)/ /sup n/ to /spl radic/(dim) for either of the lattice problems would imply the hardness of the Shortest Vector Problem in l/sub 2/ norm; an old open problem. Our proofs use reductions from few-prover, one-round interactive proof systems, either directly, or through a set-cover problem.