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 ...
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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.
TSP(1,2), the Traveling Salesman Problem with distances 1 and 2, is
the problem of finding a tour of minimum length in a complete
weighted graph where each edge has length 1 or 2. Let $d_o$ satisfy
$0<d_o<1/2$. We show that TSP(1,2) has no PTAS on the set ...
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We give a polynomial time approximation scheme (PTAS) for dense
instances of the NEAREST CODEWORD problem.
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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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.
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 >>>
