Titlebook: Combinatorial Optimization; Theory and Algorithm Bernhard Korte,Jens Vygen Textbook 20022nd edition Springer-Verlag Berlin Heidelberg 2002

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Financial Planning and BudgetingThe . 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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Financial Planning and BudgetingSuppose 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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Introduction,Let us start with two examples.

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Graphs,Graphs are a fundamental combinatorial structure used throughout this book. In this chapter we not only review the standard definitions and notation, but also prove some basic theorems and mention some fundamental algorithms.

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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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Linear Programming Algorithms,There are basically three types of algorithms for .: the . (see Section 3.2), interior point algorithms, and the ..

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

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