### Citations

14077 |
Computers and Intractability: A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ... ����¥ � such that By using this definition of the 0/1 Knapsack problem we are able to prove the NP-completeness of the problem. The 0/1 Knapsack decision problem has been proven to be NP-complete by =-=[3]-=- as well as other authors. Garey and Johnson [3] have shown that if we are able to prove that the decision statement of the problem is NP-complete, the corresponding optimization problem is also known... |

1278 |
Approximation Algorithms
- Vazirani
- 2001
(Show Context)
Citation Context ...d, the ratios can be sorted from highest to lowest ratio. When the data is sorted, you can then begin taking elements with the highest ratio until you have reached the capacity of the � knapsack [6], =-=[8]-=-. Table 1(a) shows a pre-generated data set to explore the greedy algorithm on. The algorithm’s job is to sort the data in decreasing order and this can be seen in Table 1(b). Finally a solution is ch... |

413 |
An overview of evolutionary algorithms for parameter optimization
- Bäck, Schwefel
- 1993
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Citation Context ...d change the bit of that position. The complexity of genetic algorithms has yet to be determined. It has been proven that with infinite time the genetic algorithm will converge to the correct solution=-=[2]-=-. Unfortunately, we cannot wait that long to find a solution. Because of the time complexity of finding the optimal solution we typically stop the genetic algorithm at some predetermined time. Therefo... |

231 |
Fast approximation algorithms for the knapsack and sum of subset problems,
- Ibarra, Kim
- 1975
(Show Context)
Citation Context ...ve algorithms presented here. Algorithms have been presented to improve the time complexity of the fully-polynomial approximation scheme as well as guarantee a solution closer to the optimal solution =-=[5]-=-, [7]. When choosing an algorithm to solve the 0/1 Knapsack problem, we have shown that there are different factors to consider. If we are ����� dealing with small datasets � such that , we could use ... |

194 | Complexity and approximation,
- Ausiello, Crescenzi, et al.
- 1999
(Show Context)
Citation Context ...to solve knapsack problems with large numbers of objects regardless of special rules for data sets we saw above. Unfortunately this algorithm is not complete and can be made to perform arbitrarily bad=-=[1]-=-. Consider the following problem instance ofs� £�����¡ ¡���§¨©�©�©�§ £�����¡�� £�����¡ ��� � £�����¡ ¡�� ��� � ��� � ��� ��� � � ��� defined for items. Let for all . Let , and let where � � is an arbi... |

97 |
Fast Approximation Algorithms for Knapsack Problems,
- Lawler
- 1979
(Show Context)
Citation Context ...gorithms presented here. Algorithms have been presented to improve the time complexity of the fully-polynomial approximation scheme as well as guarantee a solution closer to the optimal solution [5], =-=[7]-=-. When choosing an algorithm to solve the 0/1 Knapsack problem, we have shown that there are different factors to consider. If we are ����� dealing with small datasets � such that , we could use the b... |

10 | The 0-1 knapsack problem – an introductory survey
- Lagoudakis
- 1996
(Show Context)
Citation Context ... found, the ratios can be sorted from highest to lowest ratio. When the data is sorted, you can then begin taking elements with the highest ratio until you have reached the capacity of the � knapsack =-=[6]-=-, [8]. Table 1(a) shows a pre-generated data set to explore the greedy algorithm on. The algorithm’s job is to sort the data in decreasing order and this can be seen in Table 1(b). Finally a solution ... |

1 |
Various notions of approximations
- Houchbaum
- 1997
(Show Context)
Citation Context ...n as we go without searching through all possible combinations of solutions. This algorithm is also known as a pseudo-polynomial time algorithm for knapsack. This section borrows heavily from [8] and =-=[4]-=-. To start developing the algorithm we need to find the maximum profit possible by placing objects into the knapsack. Let be the value of the object with the highest ��� value, then is a trivial upper... |