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Electronic Colloquium on Computational Complexity

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TR08-101 | 20th November 2008 00:00

Linear Time Approximation Schemes for the Gale-Berlekamp Game and Related Minimization Problems



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.

ISSN 1433-8092 | Imprint