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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Marek Karpinski

We present some of the recent results on computational complexity

of approximating bounded degree combinatorial optimization problems. In

particular, we present the best up to now known explicit nonapproximability

bounds on the very small degree optimization problems which are of

particular importance on the intermediate stages ...
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Wenceslas Fernandez de la Vega, Marek Karpinski, Claire Kenyon

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 ...
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Marek Karpinski

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.

Amin Coja-Oghlan, Andreas Goerdt, AndrÃ© Lanka, Frank SchÃ¤dlich

Abstract. It is known that random k-SAT formulas with at least

(2^k*ln2)*n random clauses are unsatisfiable with high probability. This

result is simply obtained by bounding the expected number of satisfy-

ing assignments of a random k-SAT instance by an expression tending

to 0 when n, the number of variables ...
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