The solution to Berlekamp's switching game
Discrete Mathematics
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
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
MAX-CUT has a randomized approximation scheme in dense graphs
Random Structures & Algorithms
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Random sampling and approximation of MAX-CSP problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximating minimum unsatisfiability of linear equations
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Hardness of Bounded Degree MIN-CSP and MIN-BISECTION
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for dense instances of minimum constraint satisfaction
Random Structures & Algorithms
Fitting tree metrics: Hierarchical clustering and Phylogeny
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Sampling from large matrices: An approach through geometric functional analysis
Journal of the ACM (JACM)
Yet another algorithm for dense max cut: go greedy
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the Hardness of Decoding the Gale–Berlekamp Code
IEEE Transactions on Information Theory
A polynomial time approximation scheme for k-consensus clustering
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On approximation complexity of metric dimension problem
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Approximation schemes for the betweenness problem in tournaments and related ranking problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A randomized PTAS for the minimum Consensus Clustering with a fixed number of clusters
Theoretical Computer Science
On the parameterized complexity of consensus clustering
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Approximation complexity of Metric Dimension problem
Journal of Discrete Algorithms
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We design a linear time approximation scheme for the Gale-Berlekamp Switching Game and generalize it to a wider class of dense fragile minimization problems including the Nearest Codeword Problem (NCP) and Unique Games Problem. Further applications include, among other things, finding a constrained form of matrix rigidity and maximum likelihood decoding of an error correcting code. As another application of our method we give the first linear time approximation schemes for correlation clustering with a fixed number of clusters and its hierarchical generalization. Our results depend on a new technique for dealing with small objective function values of optimization problems and could be of independent interest.