Multivariate Algorithms for High Multiplicity Scheduling

调度与规划问题属于算法中的基本问题。这些问题中的许多是极不可能承认程序，保证提供一个最佳的解决方案在多项式时间。因此，在过去的几十年里，已经开发了数百种近似算法来解决这类问题。在这个项目中，我们处理一种替代方法来解决具有高度多重性的调度问题，其中必须计划大量的工件，这些工件可以分为几类。这种问题出现在例如着陆飞机的排序中，其安全间隔距离主要取决于各个飞机属于少数几种飞机类型中的哪一种。我们的目标是开发固定参数的算法，它提供最佳的解决方案的时间，多项式依赖于输入的大小和superpolynomially只在少数类别。这样，我们推广多项式时间算法的特殊情况下，这些问题只有不断许多工作类别更现实的模型，同时提高运行时间的固定参数算法，到目前为止，需要一个奢侈的编码的每一个单一的工作。

Scheduling and planning problems belong to the fundamental questions in algorithms. Many of those problems are highly unlikely to admit procedures that guarantee to deliver an optimal solution in polynomial time. Therefore, hundreds of approximation algorithms have been developed for such problems in the past decades.In this project we deal with an alternative approach for scheduling problems with high multiplicity, in which a large number of jobs must be planned which can be categorized into few categories. Such problems arise in, for instance, sequencing of landing aircraft, whose safety separation distances mainly depend on which of few aircraft type the respective planes belong to. Our goal is the development of fixed-parameter algorithms, which deliver optimal solutions in time that depends polynomially on the input size and superpolynomially only in the small number of categories. This way, we generalize polynomial-time algorithms for special cases of those problems with only constantly many job categories to more realistic models, and simultaneously improve the run times of fixed-parameter algorithms which so far require a lavish encoding of every single job.