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Note: On the set-union Knapsack problem. (English) Zbl 0831.90088
The authors have defined a generalization of the 0-1 knapsack problem called the set-union knapsack problem (SKP): \[ \max\Biggl\{ \sum_{i\in K} v_i \Biggl|\sum_{j\in P_K} s_j\leq b,\;K\subseteq\{1,\dots, m\}\Biggr\}, \] where \(P_i\subseteq \{1,\dots, n\}\) so that \(\bigcup^\infty_{i= 1} P_i= \{1,\dots, n\}\) and \(P_K= \bigcup_{i\in K} P_i\). They show that the SKP remains NP- hard even in very restricted cases and present an exact dynamic programming algorithm that runs in polynomial time only for special cases. Two applications of SKP are also presented: machine loading in flexible manufacturing systems and the allocations of storage to fields in a data base.

MSC:
90C10 Integer programming
90C35 Programming involving graphs or networks
90C39 Dynamic programming
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