We give the first polynomial time approximability characterization of dense weighted instances of MAX-CUT, and some other dense weighted NP-hard problems in terms of their empirical weight distributions. This gives also the first almost sharp characterization of inapproximability of unweighted 0,1 MAX-BISECTION instances in terms of their density parameter. more >>>

The Max-Bisection and Min-Bisection are the problems of finding partitions of the vertices of a given graph into two equal size subsets so as to maximize or minimize, respectively, the number of edges with exactly one endpoint in each subset. In this paper we design the first polynomial time approximation ... 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 design a polynomial time approximation scheme (PTAS) for the problem of Metric MIN-BISECTION of dividing a given finite metric space into two halves so as to minimize the sum of distances across that partition. The method of solution depends on a new metric placement partitioning method which could be ... more >>>

We prove that the subdense instances of MAX-CUT of average degree Omega(n/logn) posses a polynomial time approximation scheme (PTAS). We extend this result also to show that the instances of general 2-ary maximum constraint satisfaction problems (MAX-CSP) of the same average density have PTASs. Our results display for the first ... 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 >>>