Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - &egr;
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
Improved Inapproximability Results for Vertex Cover on k -Uniform Hypergraphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the hardness of approximating label-cover
Information Processing Letters
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
SIAM Journal on Computing
Scheduling orders for multiple product types to minimize total weighted completion time
Discrete Applied Mathematics
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Optimal Long Code Test with One Free Bit
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Order scheduling models: hardness and algorithms
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
A better approximation ratio for the vertex cover problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the inapproximability of vertex cover on k-partite k-uniform hypergraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Inapproximability of b-matching in k-uniform hypergraphs
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Information Processing Letters
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
Approximating vertex cover in dense hypergraphs
Journal of Discrete Algorithms
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
An invariance principle for polytopes
Journal of the ACM (JACM)
Approximating vertex cover using edge-based representations
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
Approximation resistance from pairwise independent subgroups
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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Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2 - ε for the problem of minimizing the total weighted completion time in concurrent open shops. We also obtain a hardness of 2 - ε for minimizing the makespan in the assembly line problem. These results follow from a new inapproximability result for the Vertex Cover problem on k-uniform hypergraphs that is stronger and simpler than previous results. We show that assuming the UGC, for every k ≥ 2, the problem is inapproximable within k - ε even when the hypergraph is almost k-partite.