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

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Understanding Financial Informationuffice to connect all cities and they should be as cheap as possible. It is natural to model the network by a graph: the vertices are the cities and the edges correspond to the cables. By Theorem 2.4 the minimal connected spanning subgraphs of a given graph are its spanning trees.
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https://doi.org/10.1007/978-1-349-18691-4apter 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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Contribution and Break-Even Analysisare 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).
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Understanding Financial Informationuffice to connect all cities and they should be as cheap as possible. It is natural to model the network by a graph: the vertices are the cities and the edges correspond to the cables. By Theorem 2.4 the minimal connected spanning subgraphs of a given graph are its spanning trees.
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