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A Parallel Algorithm for the Knapsack Problem
May 1984 (vol. 33 no. 5)
pp. 404-408
E.D. Karnin, IBM Scientific Center
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
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
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