Kellerer, Hans; Pferschy, Ulrich; Pisinger, David Knapsack problems. (English) Zbl 1103.90003 Berlin: Springer (ISBN 3-540-40286-1/hbk). xx, 546 p. (2004). The book starts with a basic introduction to the knapsack problem, the most frequently treated integer programming problem with a single constraint, where a subset of a certain number of items, each of them with its profit and weight, must be selected so that the total profit is maximized and the total weight remains below a certain capacity. It proceeds with a discussion about the basic techniques available for the solution to this problem, which makes it useful reading for undergraduate students of computer science, mathematics and economics. The remaining chapters give an overview of the generalizations of the problem as well as the advanced algorithms for its solution. The best currently available exact algorithms, both from the point of view of complexity and the running time, as well as the approximation algorithms and heuristics are presented for a number of variations of the knapsack problem. The generalizations of the problem are illustrated by some applications. This part of the book represents good reading for graduate students of computer science and mathematics, but also for a reader willing to go into more depth of the problem. At the end of the book, the authors provide a short presentation of the NP-completeness of the knapsack problem. In conclusion, it could be said that the book is a valuable source for students, but also for researchers interested in this problem. Reviewer: K. Šorić (Zagreb) Cited in 3 ReviewsCited in 553 Documents MSC: 90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming 90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming 90C10 Integer programming 90C27 Combinatorial optimization 90C59 Approximation methods and heuristics in mathematical programming 90C60 Abstract computational complexity for mathematical programming problems Keywords:knapsack problem; variants and extensions; NP-completeness; exact algorithms; approximation algorithms; heuristics Software:Knapsack PDFBibTeX XMLCite \textit{H. Kellerer} et al., Knapsack problems. Berlin: Springer (2004; Zbl 1103.90003)