Linear time approximation schemes for the Gale-Berlekamp game and related minimization problems

We design a linear time approximation scheme for the GaleBerlekamp 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. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Computations on discrete structures General Terms Algorithms, Theory Keywords Approximation Algorithms, Correlation and Hierarchical Clustering, Dense I...

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Marek Karpinski, Warren Schudy
• Keywords: Algorithms, Linear Time Approximation, Nearest Codeword Problem, STOC 2009, Time Approximation Schemes