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| 摘要: |
| 研究独立多处理机任务静态调度问题Pm|fix|Cmax,即在m个处理机系统中调度n个多处理机任务,每个任务指派到所需一组处理机上不可剥夺地执行.该问题应用广泛但早已证明为NP难问题,而且也不存在常数近似算法.分析了问题Pm|fix|Cmax和其中所有任务都是单位处理机时间的特殊情形Pm|fix,p=1|Cmax的调度,并利用实例划分(split scheduling,简称SS)、首次满足优先(first fit,简称FF)和最大宽度优先(large wide first,简称LWF)等方法,构造了问题Pm|fix,p=1|Cmax的√2m +1近似算法和问题Pm|fix|Cmax的2√m 近似算法,优于目前已有文献的最好结果. |
| 关键词: 多处理机任务调度 近似算法 近似比 NP难问题 |
| DOI： |
| 分类号: |
| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60872039, 10771060 (国家自然科学基金) |
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| Approximation Algorithm for Scheduling Independent Multiprocessor Jobs |
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HUANG Jin-Gui, LI Rong-Heng
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| Abstract: |
| This paper studies the multiprocessor job scheduling problem, and describes the m processors system, and analyze the algorithm for the problem of the offline version, both Pm|fix|Cmax of the scheduling problem with arbitrary process time jobs, and Pm|fix, p=1|Cmax of the scheduling problem with unit processing time jobs. Severalvery simple and practical polynomial time approximation algorithm are constructed, a (√2m+1)-approximation algorithm for the problem Pm|fix, p=1|Cmax and a 2√m -approximation algorithm for the problem Pm|fix|Cmax , by usingthe Split Scheduling (SS), the First Fit (FF) and the Large Wide First (LWF) technique. The results are better than any seen in the literature at present. |
| Key words: multiprocessor job scheduling approximation algorithm approximation ratio NP-hard problem |
