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Issue No.05 - May (1984 vol.33)

pp: 404-408

E.D. Karnin , IBM Scientific Center

ABSTRACT

A time?memory-processor tradeoff for the knapsack problem is proposed. While an exhaustive search over all possible solutions of an n-component knapsack requires T = 0(2n) running time, our parallel algorithm solves the problem in O(2n/2) operations and requires only 0(2n/6) processors and memory cells. It is an improvement over previous time?memory-processor tradeoffs, being the only one which outperforms the CmCs = 2" curve. Cm is the cost of the machine, i.e., the number of its processors and memory cells, and C, is the cost per solution, which is the product of the machine cost by the running time.

INDEX TERMS

VLSI complexity, Cryptography, knapsack problem, parallel architecture, time-memory-processor tradeoff

CITATION

E.D. Karnin, "A Parallel Algorithm for the Knapsack Problem",

*IEEE Transactions on Computers*, vol.33, no. 5, pp. 404-408, May 1984, doi:10.1109/TC.1984.1676456