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Vangelis Th. Paschos Editor.

## Paschos Vangelis

Paschos and Sophie Toulouse. Undetected country.

NO YES. Applications of Combinatorial Optimization, 2nd Edition. An NP-optimization problem NPO is a combinatorial optimization problem with the following additional conditions.

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This implies that the corresponding decision problem is in NP. In computer science, interesting optimization problems usually have the above properties and are therefore NPO problems. A problem is additionally called a P-optimization PO problem, if there exists an algorithm which finds optimal solutions in polynomial time. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-complete.

## Applications of Combinatorial Optimization

Note that hardness relations are always with respect to some reduction. Due to the connection between approximation algorithms and computational optimization problems, reductions which preserve approximation in some respect are for this subject preferred than the usual Turing and Karp reductions. An example of such a reduction would be the L-reduction. For this reason, optimization problems with NP-complete decision versions are not necessarily called NPO-complete.

## Combinatorial optimization - Wikipedia

NPO is divided into the following subclasses according to their approximability: [7]. From Wikipedia, the free encyclopedia. Retrieved Then divide by two because it does not matter in which direction in time they come after each other: 14! Categories : Combinatorial optimization Computational complexity theory Theoretical computer science. Hidden categories: All articles with unsourced statements Articles with unsourced statements from October Articles with unsourced statements from March Articles with unsourced statements from January Commons category link from Wikidata.

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