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

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.