Abstract This paper proves that the existence of a feasible schedule for a set of dependent tasks of unit execution times with release dates and deadlines on a limited number of processors is a fixed-parameter tractable problem. The parameter considered is the pathwidth of the interval graph associated with the time windows of the tasks. A fixed-parameter algorithm based on a dynamic programming approach is developed and proved to solve this decision problem. Fixed-parameter algorithms for the two classical problems P | p r e c , p i = 1 , r i | C max and P | p r e c , p i = 1 , r i | L max are then derived using a binary search. They are, as far as we know, the first fixed-parameter algorithms for these scheduling problems.

中文翻译：

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具有时间窗的并行机上单元相关任务调度的定参数算法

摘要 本文证明了在有限数量的处理器上，对于一组具有发布日期和截止日期的单元执行时间的依赖任务，存在可行的调度是一个固定参数的易处理问题。考虑的参数是与任务时间窗口相关的区间图的路径宽度。开发并证明了一种基于动态规划方法的固定参数算法可以解决该决策问题。两个经典问题的定参数算法 P | prec , pi = 1 , ri | C max 和 P | prec , pi = 1 , ri | 然后使用二分搜索得出 L max 。据我们所知，它们是这些调度问题的第一个固定参数算法。