Hans Kellerer, Ulrich Pferschy and David Pisinger, Knapsack Problems, Springer, Berlin (2004) ISBN 3-540-40286-1 546pp., EUR 99, 95

I cannot help but start this review with an analogy between the knapsack problem and the traveling salesman problem (TSP), the two most studied problems of combinatorial optimization. Both problems are easy to explain even to a stranger, both are hard to solve. Each of these problems is important in its own right as well as due to numerous applications. Each of the two problems forms an excellent testing ground to verify various algorithmic ideas. It is not by chance that the seminal TSP book compiled in 1985 by Lawler et al. [4] has “A guided tour of combinatorial optimization” in the title. The knapsack problem has also got its own canonical text, the famous 1990 monograph by Martello and Toth [5]. These two classical books not only give a wonderful introduction to the techniques of combinatorial optimization and their applications; they have also stimulated further research of the travelling salesman and knapsack problems, respectively. The increased volume of publications in the area and algorithmic advances that have taken place in recent years have called for another attempt to overview the developments. In 2002, the operations research community warmly received the new TSP book edited by Gutin and Punnen [1]. And now, a new book on the knapsack problem is in print. I love both TSP books and admire the work done by their editors. Still, I feel it is advantageous that unlike their TSP counterparts, both knapsack books are not edited volumes but monographs. This makes it possible to guarantee a smoother delivery, to maintain consistent notation, to organize the flow of material appropriately, e.g., in order of increasing its complexity, etc. The book under review is not simply written by people who know everything there is to know on the topic. All three authors have recently made essential contributions to the knapsack research. To mention just a few, Kellerer and Pferschy have reduced the running time and space requirements for the fully polynomial time approximation scheme for the knapsack problem [2,3]. Pisinger has improved the performance of dynamic programming algorithms using the word RAM model of computation [6]. The book under review consists of fifteen chapters. The list of quoted references exceeds 500 titles. Before looking at the structure of the book in more detail, let me make a formal statement of the knapsack problem, since this will facilitate the discussion of variants of the basic model. In its pure form, the knapsack problem is usually written as the following problem of Boolean linear programming: