On finding a minimum dominating set in a tournament (Note)
Theoretical Computer Science
Approximating clique is almost NP-complete (preliminary version)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SIAM Journal on Computing
The NP-completeness column: an ongoing guide
Journal of Algorithms
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
On the structure of parameterized problems in NP
Information and Computation
ACM SIGACT News
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
On the Amount of Nondeterminism and the Power of Verifying
SIAM Journal on Computing
On fixed-parameter tractability and approximability of NP optimization problems
Journal of Computer and System Sciences - special issue on complexity theory
Relations Among Complexity Measures
Journal of the ACM (JACM)
(poly(log log n), poly(log log n))-Restricted Verifiers are Unlikely to Exist for Languages in NP
MFCS '96 Proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science
On Limited versus Polynomial Nondeterminism
On Limited versus Polynomial Nondeterminism
\beta_k-Complete Problems and Greediness
\'beta_k-Complete Problems and Greediness
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Probabilistic checking of proofs; a new characterization of NP
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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The inapproximability of non NP-hard optimization problems is investigated. Based on self-reducibility and approximation preserving reductions, it is shown that problems LOG DOMINATING SET, TOURNAMENT DOMINATING SET and RICH HYPERGRAPH VERTEX COVER cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions are also approximable in deterministic subexponential time. A direct connection is established between non NP-hard problems and a PCP characterization of NP. Reductions from the PCP characterization show that LOG CLIQUE is not approximable in polynomial time and MAX SPARSE SAT does not have a PTAS under the assumption that SAT cannot be solved in deterministic 2O(log n√n) time and that NP ⊈ DTIME(2o(n)).