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.

In this project, the researchers develop general-purpose algorithmic methods for finding optimal and near-optimal solutions to complex multi-criteria optimization problems arising in social choice scenarios. Our algorithms will be fully multivariate to harness the structures inherent to data sets from diverse domains, and come with provable guarantees on their run time and the quality of the produced solution. With these properties, they improve upon the vast body of ad-hoc implementations currently available, which are often data-specific, or lack robust guarantees on run time and solution quality.