We study the worst-case performance guarantee of locally optimal solutions for the problem of minimizing the total weighted and unweighted completion time on parallel machine environments. Our method makes use of a mapping that maps a schedule into an inner product space so that the norm of the mapping is closely related to the cost of the schedule. We apply the method to study the most basic local search heuristics for scheduling, namely jump and swap, and establish their worst-case performance in the case of unrelated, restricted related and restricted identical machines.

中文翻译：

---

局部搜索最小调度问题的性能保证

我们研究了在并行机环境中最小化总加权和未加权完成时间的问题的局部最优解的最坏情况性能保证。我们的方法利用映射将进度表映射到内积空间，以便映射的范数与进度表的成本密切相关。我们应用该方法研究用于调度的最基本的局部搜索启发式，即跳转和交换，并在不相关、受限相关和受限相同机器的情况下建立它们的最坏情况性能。