Greedy Solvable Knapsacks - Amado, Lígia (2019)
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.