Piotr Berman, Marek Karpinski

We consider bounded occurrence (degree) instances of a minimum

constraint satisfaction problem MIN-LIN2 and a MIN-BISECTION problem for

graphs. MIN-LIN2 is an optimization problem for a given system of linear

equations mod 2 to construct a solution that satisfies the minimum number

of them. E3-OCC-MIN-E3-LIN2 ...
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Cristina Bazgan, Wenceslas Fernandez de la Vega, Marek Karpinski

It is known that large fragments of the class of dense

Minimum Constraint Satisfaction (MIN-CSP) problems do not have

polynomial time approximation schemes (PTASs) contrary to their

Maximum Constraint Satisfaction analogs. In this paper we prove,

somewhat surprisingly, that the minimum satisfaction of dense

instances of kSAT-formulas, ...
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Marek Karpinski, Warren Schudy

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 ... more >>>