Note: On the set‐union knapsack problem

Olivier Goldschmidt, David Nehme and Gang Yu

Naval Research Logistics (NRL), 1994, vol. 41, issue 6, 833-842

Abstract: We consider a generalization of the 0‐1 knapsack problem called the set‐union knapsack problem (SKP). In the SKP, each item is a set of elements, each item has a nonnegative value, and each element has a nonnegative weight. The total weight of a collection of items is given by the total weight of the elements in the union of the items' sets. This problem has applications to data‐base partitioning and to machine loading in flexible manufacturing systems. We show that the SKP remains NP‐hard, even in very restricted cases. We present an exact, dynamic programming algorithm for the SKP and show sufficient conditions for it to run in polynomial time. © 1994 John Wiley & Sons, Inc.

Date: 1994
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https://doi.org/10.1002/1520-6750(199410)41:63.0.CO;2-Q

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:41:y:1994:i:6:p:833-842

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