| 背包问题的最优并行算法 |
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| 引用本文： | 李庆华,李肯立,蒋盛益,张薇.背包问题的最优并行算法[J].软件学报,2003,14(5):891-896. |
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| 作者姓名： | 李庆华 李肯立 蒋盛益 张薇 |
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| 作者单位： | 国家高性能计算中心,武汉,湖北,武汉,430074;华中科技大学,计算机科学与技术学院,湖北,武汉,430074 |
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| 基金项目： | Supported by the National Natural Science Foundation of China under Grant No.60273075 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.863-306ZD-11-01-06 (国家高技术研究发展计划(863)); the National High Performance Computing F |
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| 摘 要： | 利用分治策略,提出一种基于SIMD共享存储计算机模型的并行背包问题求解算法.算法允许使用O(2n/4)1-ε个并行处理机单元,0≤ε≤1,O(2n/2)个存储单元,在O(2n/4(2n/4)ε)时间内求解n维背包问题,算法的成本为O(2n/2).将提出的算法与已有文献结论进行对比表明,该算法改进了已有文献的相应结果,是求解背包问题的成本最优并行算法.同时还指出了相关文献主要结论的错误.
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| 关 键 词： | 背包问题 NP完全 并行算法 分治法 |
| 文章编号： | 1000-9825/2003/14(05)0891 |
| 收稿时间： | 2002/10/28 0:00:00 |
| 修稿时间： | 2002年10月28 |
An Optimal Parallel Algorithm for the Knapsack Problem |
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| LI Qing-Hu,LI Ken-Li,JIANG Sheng-Yi and ZHANG Wei.An Optimal Parallel Algorithm for the Knapsack Problem[J].Journal of Software,2003,14(5):891-896. |
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| Authors: | LI Qing-Hu LI Ken-Li JIANG Sheng-Yi and ZHANG Wei |
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| Abstract: | A new parallel algorithm for the knapsack problem is proposed, in which the method of divide and conquer is adopted. Based on an CREW-SIMD machine with shared memory, the proposed algorithm needs O(2n/4)1-e processors, 0e1, and O(2n/2) memory to find a solution for the n-element knapsack problem in O(2n/4 (2n/4)e) time. The cost of the algorithm is O(2n/2), which is optimal and an improved result over the past researches. The wrong results in corresponding literatures are also pointed out in this paper. |
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| Keywords: | knapsack problem NP-complete parallel algorithm method of divide and conquer |
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