Titlebook: Combinatorial Optimization; Theory and Algorithm Bernhard Korte,Jens Vygen Textbook 2018Latest edition Springer-Verlag GmbH Germany, part o

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Small Water Bodies of the Western Balkansapter . 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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Small and Medium Sized Companies in Europend 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 . and write .(.) = ...(.).

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Raffaele Testorelli,Anna Tiso,Chiara Verbano (M3). In Section . we consider greedoids, arising by dropping (M2) instead. Moreover, certain polytopes related to matroids and to submodular functions, called polymatroids, lead to strong generalizations of important theorems; we shall discuss them in Section .. In Sections . and . we consider two

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The Resilience of Family Firms During Crisisare 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 polynomial-time algorithm for almost all problems discussed in this b

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Small Water Bodies of the Western Balkansapter . 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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The Resilience of Family Firms During Crisisare 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 polynomial-time algorithm for almost all problems discussed in this book (more precisely: all .-easy problems).