Improved Inapproximability Results for Vertex Cover on k -Uniform Hypergraphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Towards optimal lower bounds for clique and chromatic number
Theoretical Computer Science
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Probabilistic Proof Systems: A Primer
Foundations and Trends® in Theoretical Computer Science
Complexity of wavelength assignment in optical network optimization
IEEE/ACM Transactions on Networking (TON)
Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs
Studies in complexity and cryptography
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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For every integer k \geqslant 1, we present a PCP characterization of NP where the verifier uses logarithmic randomness, queries 4k + k2 bits in the proof, accepts a correct proof with probability 1 (i.e. it is has perfect completeness) and accepts any supposed proof of a false statement with probability at most 2^{ - k^2+ 1}. In particular, the verifier achieves optimal amortized query complexity of 1+ \delta for arbitrarily small constant 娄\delta 0. Such a characterization was already proved by Samorodnitsky and Trevisan [15], but their verifier loses perfect completeness and their proof makes an essential use of this feature.By using an adaptive verifier we can decrease the number of query bits to 2k + k2, the same number obtained in [15]. Finally we extend some of the results to larger domains.