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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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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. Are Lower Bounds Easier over the Reals? This paper has highly influenced 33 other papers.

Knapsack problem Search for additional problens on this topic. By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy PolicyTerms of Serviceand Dataset License. Citations Publications citing this paper.

Where are the hard knapsack problems? – Semantic Scholar

References Publications referenced by this paper. Skip to search form Skip to main content. Showing of extracted citations. Where are the hard knapsack problems? Topics Discussed in This Paper. Not only provlems 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.


The purpose of this paper is to give an overview of all recent exact solution approaches, and to knxpsack that the knapsack problem still is hard to solve for these algorithms for a variety of new test problems. Showing of 16 references.

Account Options Sign in. Optimizing VM allocation and data placement for data-intensive applications in cloud using ACO metaheuristic algorithm T. Knapsack problem Dynamic programming Branch and bound Pseudo-polynomial time.

Polynomial Benchmark computing Computation Code.

Where are the hard knapsack problems?

Hence, two years ago the idea arose to produce a new monograph covering pisinher 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.

Thirteen years have passed since the seminal problemz on knapsack problems by Martello and Toth appeared. From This Paper Figures, tables, and topics from this paper.


On this occasion a former colleague exclaimed back in My library Help Advanced Book Search. 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.

A time-varying transfer function for balancing the exploration and exploitation ability of a binary PSO Md.

Maringer Limited preview – Algorithm Time complexity Coefficient Experiment.

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