Knapsack ProblemsSpringer Science & Business Media, 2013年3月19日 - 548 頁 Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. On this occasion a former colleague exclaimed back in 1990: "How can you write 250 pages on the knapsack problem?" Indeed, the definition of the knapsack problem is easily understood even by a non-expert who will not suspect the presence of challenging research topics in this area at the first glance. 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. 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. 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 also more distant relatives such as multidimensional, multiple, multiple-choice and quadratic knapsack problems in dedicated chapters. |
內容
3 | 43 |
4 | 49 |
7 | 57 |
9 | 65 |
Exact Solution of the Knapsack Problem 117 | 116 |
Approximation Algorithms for the Knapsack Problem | 161 |
The Bounded Knapsack Problem | 185 |
The Unbounded Knapsack Problem 211 | 210 |
The MultipleChoice Knapsack Problem | 317 |
The Quadratic Knapsack Problem 349 | 348 |
Other Knapsack Problems | 389 |
Stochastic Aspects of Knapsack Problems | 425 |
Some Selected Applications | 449 |
A Introduction to NPCompleteness of Knapsack Problems | 483 |
References 495 | 494 |
527 | |
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常見字詞
approximation algorithm approximation schemes assume binary branch-and-bound algorithm capacity combinatorial auction complexity considered constraint core corresponding d-KP decision problem decreasing order defined denote derived described in Section dominance dynamic programming dynamic programming algorithm efficient Ext-Greedy feasible solution FPTAS given greedy algorithm greedy heuristic Hence heuristic improved inequality instance of KP integer programming item set item type iteration knapsack problem Lagrangian relaxation large items Lemma lower bound LP-relaxation Martello and Toth maximize MCKP Minknap multipliers N₁ node NP-complete number of items O(nc objective function Operations Research optimal solution value packed Pferschy Pisinger polynomial procedure profit values profits and weights PTAS recursion reduction relative performance guarantee resulting running set of items solution set solved space split item subproblem subset sum problem Theorem upper bound variables weight sum wmax worst-case