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

Authors:
D. S. Hirschberg;C. K. Wong
Affiliations:
Department of Electrical Engineering, Rice University, Houston, TX and IBM Thomas J. Watson Research Center, Yorktown Heights, New York;Computer Sciences Department, IBM Thomas J. Watson Research Center, P. O. Box 218, Yorktown Heights, NY
Venue:
Journal of the ACM (JACM)
Year:
1976

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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.