Abstract
A general-purpose parallel three-list four-table algorithm that can solve a number of knapsack-like NP-complete problems is developed in this paper. Running on an EREW PRAM model, The proposed parallel algorithm can solve this kind of problems of size n in O(n29n/20) time, with O(213n/40) shared memory units and O(2n/10) processors, and thus its time-space-processor tradeoff is O(n2 7n/8). The performance analysis and comparisons show that the proposed algorithms are both time and space efficient, and thus is an improved result over the past researches. Since it can break greater variables knapsack-based cryptosystems and watermark, the new algorithm has some cryptanalytic significance.
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References
Schroeppel, R., Shamir, A.: A T = O(2n/2), S = O(2n/4) algorithm for certain NP-complete problems. SIAM J. Comput. 10(3), 456–464 (1981)
Chor, B., Rivest, R.L.: A knapsack–type public key cryptosystem based on arithmetic in finite fields. IEEE Trans. Inform. Theory 34(5), 901–909 (1988)
Zhang, B., Wu, H.J., Feng, D.G., Bao, F.: Cyptanalysis of a knapsack based two-lock cryptosystem. In: Jakobsson, M., Yung, M., Zhou, J. (eds.) ACNS 2004. LNCS, vol. 3089, pp. 303–309. Springer, Heidelberg (2004)
Horowitz, E., Sahni, S.: Computing partitions with applications to the knapsack problem. J. ACM 21(2), 277–292 (1974)
Li, K.L., Li, Q.H., Dai, G.M.: An adaptive algorithm for the knapsack problem. Journal of Computer Development and Research 12(7), 1024–1029 (2004)
Karnin, E.D.: A parallel algorithm for the knapsack problem. IEEE Trans., Comput. 33(5), 404–408 (1984)
Amirazizi, H.R., Hellman, M.E.: Time-Memory-Processor trade-offs. IEEE Transactions on Information Theory 34(3), 505–512 (1988)
Ferreira, A.G.: A parallel time/hardware tradeoff [graphics object to be inserted manually]= O(2n/2) for the knapsack problem. IEEE Trans. Comput. 40(2), 221–225 (1991)
Chang, H.K.-C., Chen, J.J.-R., Shyu, S.-J.: A parallel algorithm for the knapsack problem using a generation and searching technique. Parallel Computing 20(2), 233–243 (1994)
Lou, D.C., Chang, C.C.: A parallel two-list algorithm for the knapsack problem. Parallel Computing 22(14), 1985–1996 (1997)
Li, K.L., Li, Q.H., Jiang, S.Y.: An optimal parallel algorithm for the knapsack problem. Journal of Software 14(5), 891–896 (2003) (in Chinese)
Aanches, C.A., Soma, N.Y., Yanasse, H.H.: Comments on parallel algorithms for the knapsack problem. Parallel Computing 28(10), 1501–1505 (2002)
Li, K.L., Li, Q.H., Li, R.F.: Optimal parallel algorithm for the knapsack problem without memory conflicts. Journal of Computer Science and Technology 19(6), 760–768 (2004)
Ferreira, A.G.: Work and memory efficient parallel algorithms for the knapsack problem. International Journal of High Speed Computing 7(4), 595–606 (1995)
Woeginger, G.J.: Space and time complexity of exact algorithms: some open problems. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 281–290. Springer, Heidelberg (2004)
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© 2005 IFIP International Federation for Information Processing
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Li, KL., Li, RF., Lei, Y., Zhou, YT. (2005). A Parallel O(n27n/8) Time-Memory-Processor Tradeoff for Knapsack-Like Problems. In: Jin, H., Reed, D., Jiang, W. (eds) Network and Parallel Computing. NPC 2005. Lecture Notes in Computer Science, vol 3779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11577188_26
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DOI: https://doi.org/10.1007/11577188_26
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