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

1976
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Journal of the ACM
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The general knapsack problem is known to be NP-complete In this paper a very special knapsack problem is studied, namely, one with only two variables. A polynomial-time algorithm is presented and analyzed However, ~t remains an open problem that for any fixed n > 2, the knapsack problem with n variables can be solved in polynomial time. KEY WORDS AND PHRASES: knapsack problem, polynomial-time algorithm, integer optimization, continued fraction approximation CR CATEGOR~S 5.25, 5.30 Introductwn

doi:10.1145/321921.321936
fatcat:bmeb6nfet5hv7cu4b2hzcj33qq