Hardness of Approximating the Closest Vector Problem with Pre-Processing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Hardness of approximate two-level logic minimization and PAC learning with membership queries
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Robust Combinatorial Optimization with Exponential Scenarios
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
The Minimum Substring Cover problem
Information and Computation
Hardness of approximate two-level logic minimization and PAC learning with membership queries
Journal of Computer and System Sciences
Approximating integer programs with positive right-hand sides
Information Processing Letters
The minimum substring cover problem
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Theoretical Computer Science
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Optimization problems in multiple subtree graphs
Discrete Applied Mathematics
Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs
Studies in complexity and cryptography
Nearly optimal NP-hardness of vertex cover on k-uniform k-partite hypergraphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Optimization problems in multiple subtree graphs
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Short witnesses and accepting lassos in ω-automata
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Approximating vertex cover in dense hypergraphs
Journal of Discrete Algorithms
Minimizing the sum of weighted completion times in a concurrent open shop
Operations Research Letters
Approximation resistance on satisfiable instances for predicates with few accepting inputs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Complexity of approximating CSP with balance / hard constraints
Proceedings of the 5th conference on Innovations in theoretical computer science
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Given a k-uniform hypergraph, the Ek-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyperedge. We present a new multilayered probabilistically checkable proof (PCP) construction that extends the Raz verifier. This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within a factor of $(k-1-\epsilon)$ for arbitrary constants $\epsilon0$ and $k\ge 3$. The result is nearly tight as this problem can be easily approximated within factor k. Our construction makes use of the biased long-code and is analyzed using combinatorial properties of s-wise t-intersecting families of subsets.We also give a different proof that shows an inapproximability factor of $\lfloor \frac{k}{2} \rfloor -\eps$. In addition to being simpler, this proof also works for superconstant values of k up to (log N)1/c, where c 1 is a fixed constant and N is the number of hyperedges.