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

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Introduction,s the machine to complete one board as fast as possible. We cannot optimize the drilling time but we can try to minimize the time the machine needs to move from one point to another. Usually drilling machines can move in two directions: the table moves horizontally while the drilling arm moves verti

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Minimum Cost Flows,apter 8 one could introduce edge costs to model that the employees have different salaries; our goal is to meet a deadline when all jobs must be finished at a minimum cost. Of course, there are many more applications.

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Weighted Matching,extend . to the weighted case and shall again obtain an .(. .)-implementation. This algorithm has many applications, some of which are mentioned in the exercises and in Section 12.2. There are two basic formulations of the weighted matching problem:

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,-Matchings and ,-Joins,ed as generalizations of the . and also include other important problems. On the other hand, both problems can be reduced to the .. They have combinatorial polynomial-time algorithms as well as polyhedral descriptions. Since in both cases the . turns out to be solvable in polynomial time, we obtain

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Matroids,nd an element of . whose cost is minimum or maximum. In the following we consider modular functions ., i.e. assume that . for all .; equivalently we are given a function .: . → ℝ and write .(.) = Σ..(.).

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,-Completeness,are also many important problems for which no polynomial-time algorithm is known. Although we cannot prove that none exists we can show that a polynomial-time algorithm for one “hard” (more precisely: .-hard) problem would imply a polynomialtime algorithm for almost all problems discussed in this bo