Fully parallelized multi prover protocols for NEXP-time (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Two-prover one-round proof systems: their power and their problems (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SIAM Journal on Computing
PCP characterizations of NP: towards a polynomially-small error-probability
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Minimum Propositional Proof Length is NP-Hard to Linearly Approximate
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Intractability of Assembly Sequencing: Unit Disks in the Plane
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
Approximation algorithms for the Label-CoverMAX and Red-Blue Set Cover problems
Journal of Discrete Algorithms
Polynomial flow-cut gaps and hardness of directed cut problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the Positive--Negative Partial Set Cover problem
Information Processing Letters
Frugal Routing on Wireless Ad-Hoc Networks
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Approximation and Hardness Results for Label Cut and Related Problems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximation and hardness results for label cut and related problems
Journal of Combinatorial Optimization
Sparse weighted voting classifier selection and its linear programming relaxations
Information Processing Letters
A note on the subadditive network design problem
Operations Research Letters
On optimal preprocessing for contraction hierarchies
Proceedings of the 5th ACM SIGSPATIAL International Workshop on Computational Transportation Science
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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The LABEL-COVER problem, defined by S. Arora, L. Babai, J. Stem, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724-733], serves as a starting point for numerous hardness of approximation reductions. It is one of six 'canonical' approximation problems in the survey of Arora and Lund [Hardness of Approximations, in: Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996, Chapter 10]. In this paper we present a direct combinatorial reduction from low error-probability PCP [Proceedings of 31st ACM Symposium on Theory of Computing, 1999, pp. 29-40] to LABEL-COVER showing it NP-hard to approximate to within 2(log n)1-o(1). This improves upon the best previous hardness of approximation results known for this problem.We also consider the MINIMUM-MONOTONE-SATISFYING-ASSIGNMENT (MMSA) problem of finding a satisfying assignment to a monotone formula with the least number of 1's, introduced by M. Alekhnovich, S. Buss, S. Moran, T. Pitassi [Minimum propositional proof length is NP-hard to linearly approximate, 1998]. We define a hierarchy of approximation problems obtained by restricting the number of alternations of the monotone formula. This hierarchy turns out to be equivalent to an AND/OR scheduling hierarchy suggested by M.H. Goldwasser, R. Motwani [Lecture Notes in Comput, Sci., Vol. 1272, Springer-Verlag, 1997, pp. 307-320]. We show some hardness results for certain levels in this hierarchy, and place LABELCOVER between levels 3 and 4. This partially answers an open problem from M.H. Goldwasser, R. Motwani regarding the precise complexity of each level in the hierarchy, and the place of LABEL-COVER in it.