Abstract
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).
This work was partially funded by the French Coordinated Research Program C 3 and by the Esprit BRA project No 3280.
Supported by a grant from the MRT.
This article was processed using the LaTEX macro package with LLNCS style
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R. Garfinkel and G. Nemhauser, Integer Programming. John Wiley and Sons, 1972.
T. C. Hu, Combinatorial Algorithms. Addison-Wesley Publishing Company, 1982.
S. Martello and P. Toth, Knapsack Problems: Algorithms and Computer Implementation. John Wiley and Sons, 1990.
M. Garey and D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1979.
R. Bellman, Dynamic Programming. Princeton University Press, Princeton, NJ, 1957.
G. Chen, M. Chern, and J. Jang, “Pipeline architectures for dynamic programming algorithms,” Parallel Computing, vol. 13, pp. 111–117, 1990.
G. Li and B. Wa, “Systolic processing for dynamic programming problems,” in Proc. International Conference on Parallel Processing, pp. 434–441, 1985.
R. J. Lipton and D. Lopresti, “Delta transformation to symplify VLSI processor arrays for serial dynamic programming,” in Proc. International Conference on Parallel Processing, pp. 917–920, 1986.
R. Andonov, V. Aleksandrov, and A. Benaini, “A linear systolic array for the knapsack problem,” Tech. Rep., Center of Computer Science and Technology, Acad. G. Bonchev st., bl. 25a, Sofia 1113, Bulgaria, 1991.
P. Quinton and Y. Robert, Algorithmes et architectures systoliques. Masson, 1989. English translation by Prentice Hall, Systolic Algorithms and Architectures, Sept. 1991.
H. T. Kung, “Why systolic architectures,” Computer, vol. 15, pp. 37–46, 1982.
S. Teng, “Adaptive parallel algorithm for integral knapsack problems,” J. of Parallel and Distributed Computing, vol. 8, pp. 400–406, 1990.
R. Andonov and F. Gruau, “A 2D modular toroidal systolic array for the knapsack problem,” in ASAP'91,(Barcelona, Spain), September 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Andonov, R., Quinton, P. (1992). Efficient linear systolic array for the knapsack problem. In: Bougé, L., Cosnard, M., Robert, Y., Trystram, D. (eds) Parallel Processing: CONPAR 92—VAPP V. VAPP CONPAR 1992 1992. Lecture Notes in Computer Science, vol 634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55895-0_419
Download citation
DOI: https://doi.org/10.1007/3-540-55895-0_419
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55895-8
Online ISBN: 978-3-540-47306-0
eBook Packages: Springer Book Archive