A processor-efficient systolic algorithm for the dynamic programming approach to the knapsack problem is presented in this paper. The algorithm is implemented on a linear systolic array where the number of the cells q, the cell memory storage α and the input/output requirements are design parameters. These are independent of the problem size given by the number of the objects m and the knapsack capacity c. The time complexity of the algorithm is Θ(mc/q + m) and both the time speedup and the processor efficiency are asymptotically optimal. A new procedure for the backtracking phase of the algorithm with a time complexity Θ(m) is also proposed. It is an improvement on the usual strategies used for backtracking which have a time complexity Θ(m + c).
CITATION STYLE
Andonov, R., & Quinton, P. (1992). Efficient linear systolic array for the knapsack problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 634 LNCS, pp. 247–258). Springer Verlag. https://doi.org/10.1007/3-540-55895-0_419
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