An efficient algorithm based on this relation for solving P is proposed. It is shown that time complexity of the algorithm is O(n log n), where n is the number of items. Finally, some further research problems
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This is why lattice-based algorithms, despite their polynomial time complexity, did not replace Berlekamp–Zassenhaus as the standard method. That is now changing; new versions of computer algebra systems such as Maple, Magma, NTL and Pari have already switched to the algorithm presented here....
We consider a special case of the unbounded knapsack problem that is characterized by a set of simple inequalities that relate item weights to item costs. We present an algorithm for this special case with time complexity linear in the number of items. ...
Analysised of the complexity of the algorithm and implementation results showed that the designed algorithm is effective and feasible. This algorithm can be extended to solve other NPC problems, such as TSP problemYan-Hua ZhongShu-Zhi Nie
A systolic algorithm for solving the O/1-knapsack problems with n items is presented. The computational model used is a tree structure which consists of 2(n) identical processing elements (PEs). Each PE executes the same program at any time step. The time complexity varies from n to 3n -...
We proposed an efficient algorithm for solving RTVKP with dynamic size of knapsack based on dynamic programming method, and analyzed the complexity of new algorithm and the condition of its successful executing. I}he results of simulation computation show that the exact algorithm is an efficient ...
, but it can never be below 1 . 693 . in the advice complexity setting, we measure how many bits of information (so-called advice bits) the algorithm has to know to achieve some desired solution quality. for the simple unbounded knapsack problem, one advice bit lowers the competitive ...
Frieze and Clarke [79] gave a PTAS for d-dimensional knapsack using the dual simplex algorithm for LP. Subsequently, Caprara et al. [174] gave a scheme with improved running time of O(n⌈d/ε⌉−d). However, there is no EPTAS even for 2-D vector knapsack [80], unless W[1...
However, it seems that this is a futile exercise with little hope for an overall improved running time complexity. 6. Computational experiments In this section we computationally evaluate, on a large set of instances, the dynamic programming algorithm of Section 2 and the other exact algorithms ...