Titlebook: Complexity and Approximation; Combinatorial Optimi Giorgio Ausiello,Alberto Marchetti-Spaccamela,Vigg Textbook 1999 Springer-Verlag Berlin

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The Complexity of Optimization Problems,set of . and . is the set of .. As an alternative view, we can also consider a predicate .(x,y) which is true if and only if (x,y) ∈ .. If we want to analyze the properties of the computations to be performed, it is necessary to consider the characteristics of the sets ., . and of the relation . (or of the predicate .) more closely.

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Input-Dependent and Asymptotic Approximation,proximation algorithm but no approxima-tion scheme exists (unless P=N.). To deal with these two latter kinds of problem, in this chapter we will relax the constraint on the performance ratio in two ways.

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Approximation Preserving Reductions,eductions not always preserve the measure function and, even if this happens, they rarely preserve the quality of the solutions. It is then clear that a stronger kind of reducibility has to be used that not only maps instances of a problem .. to instances of a problem .., but it also maps back good solutions for .. to good solutions for ...

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