Titlebook: Combinatorial Optimization; Theory and Algorithm Bernhard Korte,Jens Vygen Textbook 20084th edition Springer-Verlag Berlin Heidelberg 2008

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Quentin Thuillier,Isabelle Behm-AnsmantIn this and the next chapter we consider flows in networks. We have a digraph . with edge capacities . : .(.) → ℝ. and two specified vertices s (the .) and . (the .). The quadruple (.) is sometimes called a ..

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condescend

https://doi.org/10.1007/978-1-4757-6523-6In this chapter we introduce the important concept of approximation algorithms. So far we have dealt mostly with polynomially solvable problems. In the remaining chapters we shall indicate some strategies to cope with .-hard combinatorial optimization problems. Here approximation algorithms must be mentioned in the first place.

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https://doi.org/10.1007/978-3-642-74913-1The . and the . discussed in earlier chapters are among the “hardest” problems for which a polynomial-time algorithm is known. In this chapter we deal with the following problem which turns out to be, in a sense, the “easiest” .-hard problem:

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Markus Kuhlmann,Blaga Popova,Wolfgang NellenSuppose we have . objects, each of a given size, and some bins of equal capacity. We want to assign the objects to the bins, using as few bins as possible. Of course the total size of the objects assigned to one bin should not exceed its capacity.

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Linear Programming,In this chapter we review the most important facts about Linear Programming. Although this chapter is self-contained, it cannot be considered to be a comprehensive treatment of the field. The reader unfamiliar with Linear Programming is referred to the textbooks mentioned at the end of this chapter.

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Integer Programming,In this chapter, we consider linear programs with integrality constraints:

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