The classical knapsack problem is defined as follows: We are given a set of n items, . Using this concept, Pisinger  introduced a dynamic programming. Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. On this occasion a former colleague exclaimed back . The knapsack problem is believed to be one of the “easier” NP-hard D. Pisinger/Computers & Operations Research 32 () –
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Where are the hard knapsack problems? – Semantic Scholar
From This Paper Figures, tables, and topics from this paper. Showing of extracted citations. Optimizing VM allocation and data placement for data-intensive applications in cloud using ACO metaheuristic algorithm T. Polynomial Benchmark computing Computation Code.
Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared.
Maringer Limited preview – Skip to search form Skip to main content. Knapsack problem Dynamic programming Branch and bound Pseudo-polynomial time.
Showing of pproblems references. Are Lower Bounds Easier over the Reals? On this occasion a former colleague exclaimed back in A time-varying transfer function for balancing the exploration and exploitation ability of a binary PSO Md.
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Hence, two years ago the idea arose to produce a new monograph covering not only the most recent developments of the standard knapsack problem, but also giving a comprehensive treatment of the whole knapsack family including the siblings such as the subset sum problem and the bounded and unbounded knapsack problem, and knapsavk more distant relatives such as multidimensional, multiple, multiple-choice and quadratic knapsack problems in dedicated chapters.
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Topics Discussed in This Paper. This paper has highly influenced 33 other papers. However, in the last decade a large number of research publications contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes.
Citations Publications citing this paper. Where are the hard knapsack problems?
Knapsack Problems – Hans Kellerer, Ulrich Pferschy, David Pisinger – Google Books
Not only can it be solved in pseudo-polynomial time, but also decades of algorithmic improvements have made it possible to solve nearly all standard instances from the literature.
Moreover, the extension of the knapsack problem to higher dimensions both in the number of constraints and in the num ber of knapsacks, as well as the modification of the problem structure concerning the knapsaxk item set and the objective function, leads to a number of interesting variations of practical relevance which were the subject of intensive research during the last few years.
The purpose of this paper is to give an overview of all recent exact solution approaches, and to show that the knapsack problem still is hard to solve for these algorithms for a problemw of new test problems.