We study dense instances of several covering problems. An instance of the set cover problem with $m$ sets is dense if there is $\epsilon>0$ such that any element belongs to at least $\epsilon m$ sets. We show that the dense set cover problem can be approximated with the performance ratio ... more >>>

We survey recent results on the existence of polynomial time approximation schemes for some dense instances of NP-hard optimization problems. We indicate further some inherent limits for existence of such schemes for some other dense instances of the optimization problems. more >>>

We give a polynomial time approximation scheme (PTAS) for dense instances of the NEAREST CODEWORD problem. more >>>

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, and linear equations ... more >>>

We survey some recent results on the complexity of computing approximate solutions for instances of the Minimum Bisection problem and formulate some intriguing and still open questions about the approximability status of that problem. Some connections to other optimization problems are also indicated. more >>>

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 >>>