Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Construction of extractors using pseudo-random generators (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Information and Computation
Fast parallel heuristics for the job shop scheduling problem
Computers and Operations Research
Clique Is Hard to Approximate within n1-o(1)
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Towards a Predictive Computational Complexity Theory
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the hardness of approximating N P witnesses
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
On Various Cooling Schedules for Simulated Annealing Applied to the Job Shop Problem
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Towards optimal lower bounds for clique and chromatic number
Theoretical Computer Science
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
The Complexity of Ferromagnetic Ising with Local Fields
Combinatorics, Probability and Computing
Inapproximability of the Tutte polynomial
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Inapproximability of the Tutte polynomial
Information and Computation
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
Random Structures & Algorithms
Shortest Path and Maximum Flow Problems in Networks with Additive Losses and Gains
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Approximating the number of frequent sets in dense data
Knowledge and Information Systems
Proceedings of the 13th International Conference on Database Theory
Approximating the partition function of the ferromagnetic Potts model
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Shortest path and maximum flow problems in networks with additive losses and gains
Theoretical Computer Science
On the approximation complexity hierarchy
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Journal of the ACM (JACM)
On obtaining pseudorandomness from error-correcting codes
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Better inapproximability results for maxclique, chromatic number and min-3lin-deletion
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Geometric aspects related to solutions of #kSAT
MICAI'05 Proceedings of the 4th Mexican international conference on Advances in Artificial Intelligence
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
The complexity of approximately counting stable roommate assignments
Journal of Computer and System Sciences
Hardness of approximation for quantum problems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximating the partition function of the ferromagnetic Potts model
Journal of the ACM (JACM)
Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials
Journal of Computer and System Sciences
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We prove that all of Karp's 21 original $NP$-complete problems have a version that is hard to approximate. These versions are obtained from the original problems by adding essentially the same simple constraint. We further show that these problems are absurdly hard to approximate. In fact, no polynomial-time algorithm can even approximate $\log^{(k)}$ of the magnitude of these problems to within any constant factor, where $\logk$ denotes the logarithm iterated $k$ times, unless $NP$ is recognized by slightly superpolynomial randomized machines. We use the same technique to improve the constant $\epsilon$ such that MAX CLIQUE is hard to approximate to within a factor of $n^\epsilon$. Finally, we show that it is even harder to approximate two counting problems: counting the number of satisfying assignments to a monotone 2SAT formula and computing the permanent of $-1$, $0$, $1$ matrices.