The classical knapsack problem is defined as follows: We are given a set of n items, . Using this concept, Pisinger [11] 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

Maringer Limited preview – Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy PolicyTerms of Serviceand Dataset License.

However, in the last decade a large number of research proglems contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes. Polynomial Benchmark computing Computation Code.

Are Lower Bounds Easier over the Reals? Citations Publications citing this paper. Hence, two years ago the idea arose to produce a new monograph knxpsack 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 also more distant relatives such as multidimensional, multiple, multiple-choice and quadratic knapsack problems in dedicated chapters.

Optimizing VM allocation and data placement for data-intensive applications in cloud using ACO metaheuristic algorithm T. References Publications referenced by this paper.

## Where are the hard knapsack problems?

From This Paper Figures, tables, and topics from this paper. Algorithm Time complexity Coefficient Experiment.

User Review – Flag as inappropriate good. Topics Discussed in This Paper. A time-varying transfer function for balancing the exploration and exploitation ability of a binary Piwinger Md.

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. Showing of extracted citations. On this occasion a former colleague exclaimed back in 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 available 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.

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### Knapsack Problems – Hans Kellerer, Ulrich Pferschy, David Pisinger – Google Books

Where are the hard knapsack problems? Showing of 16 references. Knapsack problem Search for additional papers on this topic. Knapsack problem Dynamic programming Branch and bound Pseudo-polynomial time. Skip to search form Skip to main content. Account Options Sign in. Proble,s paper has highly influenced 33 other papers. 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 variety of new test problems.