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| 背包问题的最优并行算法 |
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李庆华1,2, 李肯立1,2, 蒋盛益1,2, 张薇1,2
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1.国家高性能计算中心,武汉,湖北,武汉,430074;2.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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| 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. |
| 关键词: 背包问题 NP完全 并行算法 分治法 |
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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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| An Optimal Parallel Algorithm for the Knapsack Problem |
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LI Qing-Hua,LI Ken-Li,JIANG Sheng-Yi,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-ε processors, 0≤ε≤1, and Oi>O(2n/2) memory to find a solution for the n-element knapsack problem in O(2n/4(2n/4)ε) 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. |
| Key words: knapsack problem NP-complete parallel algorithm method of divide and conquer |
