Optimal parallel algorithm for the knapsack problem without memory conflicts

Authors:
Ken-Li Li;Ren-Fa Li;Qing-Hua Li
Affiliations:
School of Computer and Communication, Hunan University, Changsha 410082, P.R. China and School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, P.R. ...;School of Computer and Communication, Hunan University, Changsha 410082, P.R. China;School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
Venue:
Journal of Computer Science and Technology
Year:
2004

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Abstract

The knapsack problem is well known to be NP-complete. Due to its importance in cryptosystem and in number theory, in the past two decades, much effort has been made in order to find techniques that could lead to practical algorithms with reasonable running time. This paper proposes a new parallel algorithm for the knapsack problem where the optimal merging algorithm is adopted. The proposed algorithm is based on an EREW-SIMD machine with shared memory. It is proved that the proposed algorithm is both optimal and the first without memory conflicts algorithm for the knapsack problem. The comparisons of algorithm performance show that it is an improvement over the past researches.