2011•Journal of Nanyang Institute of TechnologyRequires access

THE ANALYSIS OF THE DYNAMIC PROGRAMMING FOR 0-1 KNAPSACK

Chunguang Zhou

Abstract

The 0-1 knapsack problem is a NP-hard problem,and many problems in real life can translate into it.Here 0-1 knapsack problem is described firstly,and then presents dynamic programming to solve the problem according to the properties of optimal substructure and sub-problem overlap.In addition,an improved algorithm is presented to decrease the complexity of the dynamic programming.Instance results show these algorithms are effective,and also confirm the improved algorithm is better.

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Key concepts: Knapsack problem, Dynamic programming, Continuous knapsack problem, Change-making problem, Cutting stock problem, Mathematical optimization, Substructure, Optimal substructure