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Proof verification and hardness of approximation problems
TLDR
The authors improve on their result by showing that NP=PCP(logn, 1), which has the following consequences: (1) MAXSNP-hard problems do not have polynomial time approximation schemes unless P=NP; and (2) for some epsilon >0 the size of the maximal clique in a graph cannot be approximated within a factor of n/sup ePSilon / unless P =NP. Expand
Proof verification and the hardness of approximation problems
TLDR
It is proved that no MAX SNP-hard problem has a polynomial time approximation scheme, unless NP = P, and there exists a positive ε such that approximating the maximum clique size in an N-vertex graph to within a factor of Nε is NP-hard. Expand
On the hardness of approximating minimization problems
TLDR
It is proved that there is an c >0 such that Graph Coloring cannot be approximated with ratio n’ unless P=NP unless NP is contained in DTIME[nPOIY log ~ ]. Expand
Non-deterministic exponential time has two-prover interactive protocols
TLDR
It is shown that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time and that to prove membership in languages inEXP, the honest provers need the power ofEXP only. Expand
On the hardness of approximating minimization problems
TLDR
It is proved that there is an e > 0 such that Graph Coloring cannot be approximated with ratio n e unless P = NP, and Set Covering cannot be approximation with ratio c log n for any c < 1/4 unless NP is contained in DTIME(n poly log n). Expand
Algebraic methods for interactive proof systems
TLDR
This technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system and played a pivotal role in the recent proofs that IP = PSPACE and MIP = NEXP. Expand
Hardness of approximations
An information-theoretic approach to traffic matrix estimation
TLDR
This paper presents a new approach to traffic matrix estimation using a regularization based on "entropy penalization", which chooses the traffic matrix consistent with the measured data that is information-theoretically closest to a model in which source/destination pairs are stochastically independent. Expand
Algebraic methods for interactive proof systems
TLDR
The technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system and has implications for program checking, verification, and self-correction. Expand
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