Abstract: This paper studies the problem of scheduling a set of n independent multiprocessor jobs with prespecified processor allocation on a set of identical processors in order to minimize the makespan.The problem P_mfixC_max is proved to be NP-hard and cannot be approximated within a constant factor unless P=NP.Recently，E.Bampis et al. have given a 3m^-2-approximation algorithm for this problem by using the split-round technique.This paper proposes a 2(2m^)-2-approximation algorithm for this problem based on the improvement of the split-round algorithm.

Key words: multiprocessor job scheduling, approximation algorithm, NP-hard problem

摘要： 研究多处理机任务调度模型P_mfixC_max，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。在E.Bampis等人提出的Split-Round技术基础上，提出了该问题的一个改进的多项式时间近似算法，并从理论上证明了该算法在最坏情况下的近似比为2(2m)^-2，优于E.Bampis等人给出的3m^-2的结果。

关键词: 多处理机任务调度, 近似算法, NP难问题