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 ... 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 ... more >>>

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

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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, ... 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 ... 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 ... 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.

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