Abstract: This paper studies the problem of scheduling model P_m|fix，p_j=1|C_max，that schedules a set of n independent multiprocessor jobs with unit process time and prespecified processor allocation on a set of identical processors in order to minimize the makespan.The general problem P_m|fix|C_max，that has widely been used in various fields such as the network parallel computing，the multi-casting system and the project plan，is proved to be NP-hard and cannot be approximated within a constant factor unless P=NP.This paper proposes an approximation algorithm for this problem based on the approximation clique partition method.By the analysis from test data，this algorithm presents more optional ratio preference.

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

摘要： 研究多处理机任务调度模型P_m|fix，p_j=1|C_max，即在m个处理机系统中调度n个时间长度都为1的多处理机任务，每个任务指派到所需一组处理机上不可剥夺地执行。这类问题在网络并行计算、多播系统及工程规划等领域都有广泛的应用，但早已被证明为NP难问题，而且也不存在常数近似算法。基于团划分方法构造了该问题的多项式时间近似算法，通过模拟实验进行了验证，和最大宽度优先（LWF）算法相比，该算法花费时间较长，近似比性能要好。

关键词: 多处理机任务, 调度, 近似算法, NP难问题, 团划分