2log1-ε n hardness for the closest vector problem with preprocessing

Authors:
Subhash A. Khot;Preyas Popat;Nisheeth K. Vishnoi
Affiliations:
New York University, New York, NY, USA;New York University, New York, NY, USA;Microsoft Research, Bangalore, India
Venue:
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Year:
2012

Citing 19
Cited 1

A hierarchy of polynomial time lattice basis reduction algorithms

Theoretical Computer Science
Algebraic methods for interactive proof systems

Journal of the ACM (JACM)
The hardness of approximate optima in lattices, codes, and systems of linear equations

Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP

Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems

Journal of the ACM (JACM)
A Parallel Repetition Theorem

SIAM Journal on Computing
Hardness Results for Coloring 3 -Colorable 3 -Uniform Hypergraphs

FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximating CVP to Within Almost-Polynomial Factors is NP-Hard

Combinatorica
The inapproximability of lattice and coding problems with preprocessing

Journal of Computer and System Sciences - Special issue on computational complexity 2002
Lattice problems in NP ∩ coNP

Journal of the ACM (JACM)
Hardness of Approximating the Closest Vector Problem with Pre-Processing

FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Lattice problems and norm embeddings

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Agnostic Learning of Monomials by Halfspaces Is Hard

FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A deterministic single exponential time algorithm for most lattice problems based on voronoi cell computations

Proceedings of the forty-second ACM symposium on Theory of computing
On the hardness of learning intersections of two halfspaces

Journal of Computer and System Sciences
Better inapproximability results for maxclique, chromatic number and min-3lin-deletion

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Hardness of Approximating the Closest Vector Problem with Pre-Processing

Computational Complexity - Special issue in memory of Misha Alekhnovich
Improved inapproximability of lattice and coding problems with preprocessing

IEEE Transactions on Information Theory

Universal factor graphs

ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that for an arbitrarily small constant ε0, assuming NP⊈ DTIME (2logO 1-ε n), the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than 2log1-ε n. This improves upon the previous hardness factor of (log n)δ for some δ0 due to [AKKV05].