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).