When is a 0-1 knapsack a matroid?
Wolsey gave a necessary and sufficient condition for the set of the feasible solutions of an arbitrary 0-1 knapsack to be a matroid. However, from that condition a polynomial time algorithm does not directly follow. Recently Amado and Barcia showed how matroids can be used, within a lagrangean relaxation approach, to obtain strong bounds for 0-1 knapsacks. They described a polynomial time algorithm to decide whether a knapsack is a member of a special family of matroids. Yet knapsacks exist which are matroids and do not belong to that family. Here we give a polynomial time algorithm to decide whether an arbitrary 0-1 knapsack is a matroid. We also show that, unless P = NP, there is no polynomial time algorithm for deciding whether the greedy algorithm produces a maximum weight solution for a 0-1 knapsack problem.
- OSTI ID:
- 35806
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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