Greedy Solvable Knapsacks
The family K of the feasible solutions for a 0-1 Knapsack with positive coefficients, K={l⊂N:Σi∈Iai≤b}, is an independence system over N={1,...,n}. In some cases, for instance when all the ai have the same value, this independence system is a matroid over N. We will say then that the knapsack is gre...
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| Formato: | workingPaper |
| Idioma: | eng |
| Publicado em: |
2019
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| Texto completo: | http://hdl.handle.net/10362/85388 |
| País: | Portugal |
| Oai: | oai:run.unl.pt:10362/85388 |
| Resumo: | The family K of the feasible solutions for a 0-1 Knapsack with positive coefficients, K={l⊂N:Σi∈Iai≤b}, is an independence system over N={1,...,n}. In some cases, for instance when all the ai have the same value, this independence system is a matroid over N. We will say then that the knapsack is greedy solvable. In this paper We study the conditions for a knapsack to be greedy solvable. We present necessary and sufficient conditions, verifiable in polynomial time, for K to be a member of a finite family of matroids over N. |
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