A Polynomial-Time Algorithm for the Knapsack Problem with Two Variables

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Abstract

The general knapsack problem is known to be NP-complete. In this paper a very special knapsack problem ia studied, namely, one with only two variables. A polynomial-time algorithm is presented and analyzed. However, it remains an open problem that for any fixed n > 2, the knapsack problem with n variables can be solved in polynomial time. © 1976, ACM. All rights reserved.

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Hirschberg, D. S., & Wong, C. K. (1976). A Polynomial-Time Algorithm for the Knapsack Problem with Two Variables. Journal of the ACM (JACM), 23(1), 147–154. https://doi.org/10.1145/321921.321936

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