Abstract
Integer programs are very hard to solve. Even the knapsack problem, one of the simplest integer programs, is NP-complete. In order to solve this problem, most people would use the dynamic programming-type algorithm of Gilmore and Gomory. This algorithm is pseudo-polynomial and has time complexity O(nb), where b is the weight-carrying capacity of the knapsack. The knapsack problem can also be solved using Landa’s algorithm, as we saw in Sect. 8.2. Landa’s algorithm is also pseudo-polynomial and has time complexity O(nw 1), where w 1 is the weight of the best item.
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© 2016 Springer International Publishing Switzerland
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Hu, T.C., Kahng, A.B. (2016). The World Map of Integer Programs. In: Linear and Integer Programming Made Easy. Springer, Cham. https://doi.org/10.1007/978-3-319-24001-5_10
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DOI: https://doi.org/10.1007/978-3-319-24001-5_10
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-24001-5
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